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The horse Stuart Coltherd couldn't sell is in the Grand National | Daily Mail Online
Stuart Coltherd used to ride just to round up the sheep on his 600-acre farm. Now the horse he couldn't sell is in the Grand National and gunning to be another great Scot
Stuart Coltherd's star horse will race in the £1m Randox Health Grand National
Captain Redbeard who will be ridden by son Sam and led up by daughter Amy
The odds may seem stacked against the small family operation and 40-1 shot
Published: 17:37 EST, 7 April 2018 | Updated: 05:19 EST, 8 April 2018
Spring is a very busy time for Stuart Coltherd. There are 600 acres to farm and more than 100 ewes about to start lambing. That is not any easier when snow is still arriving and giving Easter a Christmas card feel at your Scottish Border base.
Then, on top of all that, there is a £1million Randox Health Grand National to try to win with the star horse among your 22-strong string. No wonder Coltherd, 51, said with a degree of understatement: 'It's all hands on deck!'
It certainly will be if his nine-year-old gelding Captain Redbeard, who will be ridden by Coltherd's 19-year-old son Sam and led up by daughter Amy, 20, can win Saturday's race at Aintree.
Stuart Coltherd (right) with his son Sam and Grand National hope Captain Redbeard
In a jump racing world increasingly dominated by the big stables and in the aftermath of a Cheltenham Festival full of Irish winners, the odds may seem stacked against the small family operation and Captain Redbeard, far longer than the 40-1 most bookmakers are quoting.
But that would be to forget the Grand National's fierce unpredictability and ignore the rapid rise through the ranks this season of a horse Coltherd believes is the best he has ever trained.
Bryony Frost aims to follow in her father's footsteps in... BHA to carry out a review after six horse deaths at... As De Mee out of Randox Health Grand National leaving Paul... Cesarewitch hits jackpot as Newmarket set to announce raft...
Coltherd has also confounded the odds at Aintree before. In 2013, he saddled Tartan Snow to win the Foxhunters' Chase, the race for amateur jockeys over the famous Grand National fences, at 100-1.
'That was a hell of a day,' said Coltherd. 'We never thought he was a 100-1 shot, we thought he was better than that. It was after that I thought you should never be frightened to go for some of these races. You have to have a little bit of faith in your own judgment, take the chance and go for it.'
Captain Redbeard finished sixth in the Grand Sefton Chase at Aintree in December when a horse fell in front of him four out and stopped him in his tracks. But going for the National had not crossed Coltherd's mind at that stage.
Captain Redbeard who will be ridden by son Sam and led up by daughter Amy at Aintre
He was regarded as a horse for far shorter distances than the National's four-mile, two-furlong marathon. But fate, in the guise of this winter's bad weather, intervened, reduced racing opportunities and forced the trainer to take a chance.
Coltherd said: 'The snow and frost never seem to have stopped. We had well over a foot of snow at one time. We are about 850ft above sea level. If you see snow on the hills, it is usually snow with us. We always thought Captain Redbeard was a horse better over two-mile five furlongs or two-mile six furlongs and on better ground. It's just there weren't that many races for him.
'It was just luck that we entered him in the Tommy Whittle Chase at Haydock over three miles on heavy ground. The day before I did think, 'Why are we going there? He'll never do anything in that' — but he won quite easily.
'He went up in the handicap and ran a good race over three and a quarter miles back at Haydock in the Peter Marsh Chase. It was then we decided to go for the National.'
That prompted son Sam, who has played his part in calming the initially wayward Captain Redbeard and recalls an effortless first win on him at an Alnwick point-to-point in March 2015, to make an urgent call to the BHA to make sure he was eligible to ride.
The odds may seem stacked against the small family operation and Captain Redbeard
Sam, who has ridden 31 winners under rules and whose only other ride over the Aintree fences was finishing eighth on Ockey De Neulliac in the 2016 Foxhunters' Chase, said: 'I was straight on the phone — I even rang them twice just to reassure myself.'
Coltherd Snr's original contact with horses had nothing to do with racing, just rounding up the sheep before quad bikes — 'They're much quicker' — came along. But that led to show jumping and then point-to-pointing and the racing bug was sown. His first winner, £700 buy Murder Moss, who won at Hexham in 1999, is still grazing in a field on his Selkirkshire farm at 32.
Coltherd bought Captain Redbeard off his original owner — 'I paid as much as I could afford at the time but I wanted to keep him' — and patiently brought him through the ranks. Initial attempts to sell the gelding proved fruitless. That would not be the case now. 'I tried to sell him so many times to different owners, I couldn't get anyone to buy him, so I just kept him myself', he said.
'I have had a couple of people phone up since it was decided he was going for the National but I thought, 'I've had him this long so why sell now'?' Twelve months ago, Lucinda Russell-trained One For Arthur became only the second Scottishtrained Grand National winner.
Coltherd said: 'Lucinda has always given me plenty of encouragement and support and said, given what Captain Redbeard has done, I should go for the National. 'It's a massive day. We are lucky to find a horse as good as him. You can pay all the money in the world but finding them is the hard thing.'
Coltherd will be accompanied to Aintree by 16-year-old daughter Milly, who also helps out at the family stable, but wife Lesley is threatening to give it a miss - 'She gets too nervous'. For Sam, who is based with trainer Sue Smith and her husband Harvey, it will be the first time he has attended a Grand National.
He watched One For Arthur's win from home but has viewed a re-run a few times and plans to get advice from his jockey Derek Fox. Sam will also speak to his friend and Scottish neighbour Ryan Mania, who won the 2013 National on Auroras Encore, and his coach, former jockey Brian Harding. 'This is the biggest ride I've ever had and probably will be for a while after it,' said Sam. '
Everyone is getting excited at home. We might only be a small operation but it is a big operation for us. Jeez, I can't wait.'
Captain Redbeard is not the only horse representing Scotland. Seeyouatmidnight, third in the 2016 Scottish National, represents Sandy Thomson, who once played rugby for Scotland B, facing New Zealand and Australian teams playing for South of Scotland.
The horse Stuart Coltherd couldn't sell is in the Grand National

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The Trail Book by Mary Austin, Paperback | Barnes & Noble
Mary Austin was an early ecologist, feminist, and desert dweller. Her family moved to California in 1888 and established a homestead in the San Joaquin Valley. Her first play, The Arrowmaker, about Indian life, was produced at the New Theatre, (New York) in 1911. First published in 1918, The Trail Book is now considered a classic of American nature writing. Set in a

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Eugene Severson - Find A Grave Memorial
145098 · View Source
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Find A Grave, database and images (https://www.findagrave.com : accessed ), memorial page for Eugene Severson (unknown–unknown), Find A Grave Memorial no. 145098, citing Taylorsville Memorial Park Cemetery, Taylorsville, Salt Lake County, Utah, USA ; Maintained by Burnt Almond Fudge (contributor 46857451) .
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Brethren Evangelist, The (1987) : Winfield, Richard C. : Free Download & Streaming : Internet Archive
Brethren Evangelist, The (1987)
[archiveorg brethrenevangel109111winf width=560 height=384 frameborder=0 webkitallowfullscreen=true mozallowfullscreen=true]
Graphic Violence Graphic Sexual Content Spam, Scam or Fraud Broken or Empty Data textsBrethren Evangelist, The (1987) by Winfield, Richard C. Published 1987
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Volume Vol. 109 : No. 1-11

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The 10 Closest Vacation Rentals to The Children's Museum of the Treasure Coast, Jensen Beach on TripAdvisor
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Dinner at the Square: A Free Market for Education? Tickets, Wed, Feb 28, 2018 at 6:45 PM | Eventbrite
Wed, February 28, 2018, 6:45 PM – 8:30 PM EST
A Free Market for Education?
Charter schools vs. public schools vs. private schools. It’s a constant discussion of who does it better and more cost effectively. With vouches expanding, charter schools on the rise and free education online (Khan academy), does our education need to revamp itself?
We’re taking a dive into the economics of education. What is the impact of the privatization on the public education system and what effects does it have on the different types of population it’s serving.
For reading material and additional information about this event please visit: http://broward.villagesquare.us/event/education/
Robert Runcie, Superintendent, School Board of Broward County
Pre-Registered Guests: $35. Ticket prices will increase to $45 after 2/14/2018
Dinner at the Square: A Free Market for Education? at Funky Buddha Brewery

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Tillys Locations & Hours Near Valencia, CA - YP.com
Valencia, CA Tillys
27027 Mcbean PkwyValencia, CA 91355
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From Business: Established in Southern California in 1982, Tilly's is one of the leading specialty retailers in the action sports industry. It specializes in selling an assortme…
19811 Rinaldi StPorter Ranch, CA 91326
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All 5 of us can always find something to buy in Tillys!! The employees are super friendly and always willing to help!
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This boutique is the best in town. SO cute and SO sweet. They have truly affordable pieces that are high quality and fit great. My favorite place to shop in SCV.
slarrington74 rated
GREAT place for updating the wardrobe!! I walked in to check out the clothing as I was tired of feeling frumpy and dumpy with all the worn out maternity clothes in my closet from my 3 kids. I was helped by an AWESOME girl named Carmen. From the moment I walked in dazed and confused, she was amazing. After briefly explaining my debacle, she was so nice, helpful (without being pushy) and got it. She was like my own personal stylist. I can't wait to go back and shop for more clothes after I lose my left over baby weight.....and those last 5 rows of Oreo cookies.The only down side to the clothes I bought was that they are all dry clean only, because the fabrics are Rayon. But, that's what today's fashion is - silk and rayon tops. Just don't wear them out and spill white wine on them!! One of my brand new tops is probably ruined now because I cannot wash it or it will shrink...but that has nothing to do with the store itself. I would definitely go back to this store. The other gals I met when I was shopping were so nice too! I have no idea what the other reviewer's opinion is based on...but it says something about the store when the representative offers to contact her and resolve the issue! If I were her, I would have called the manager when I got home and explained my discontent. But, this is the internet and you can't always trust the sources from the internet (insert State Farm commercial here). For all we know, she could be from a competing store?! Anyway, I highly recommend this store to anyone! Great pieces, great prices and fabulous sales associates!!! I'm sure I will be happy with anyone, but I prefer to see Carmen again next time I shop.

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Eagle Automotive in Anchorage, AK with Reviews - YP.com
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text:
Strong Chinese Manufacturing Data Points to Turnaround
In China, new orders for exports picked up speed in September. Above, a shoe factory in Fujian province.CreditCreditAgence France-Presse — Getty Images
HONG KONG — A China manufacturing index hit its highest level in six months on Monday, offering the first important measure of how the country’s economy performed in September and showing that a tentative reacceleration has continued as government support and firmer demand for Chinese exports have gained traction.

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P. 1spm 2015spm 2015Ratings: (0)|Views: 58
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- Spieth shows that talent tops the system
ORLANDO, Fla. -- Except for the size and noise level of the crowd, and the significance of the stage, the moment was reminiscent of 17-year-old Justin Rose chipping in on the final hole at Royal Birkdale in 1998 to tie for fourth in the British Open.
That was the same year another polished talent from Dallas who went to the University of Texas -- Justin Leonard -- turned pro and did well enough in seven starts to earn a PGA Tour card without ever going to Q-school.
Spieth still has a ways to go. He probably needs another $150,000 or so to secure a full card for next year. He technically would not fall into that group of players who never went to Q-school -- Gary Hallberg, Tiger Woods, Phil Mickelson, Leonard, Ryan Moore and Bud Cauley -- because Spieth failed to get out of the second stage last year when his putter let him down. He was still an amateur, still a Longhorn.
"I thought my focus was going to be on the Web.com Tour for the year, and now my focus is out here," he said. "It's a nice change."
He took care of the rest on Sunday. The special temporary membership means Spieth can take unlimited exemptions the rest of the season, and that should be no trouble. He already is committed to play three times in Texas -- the Houston Open, Texas Open and Byron Nelson -- and more exemptions are sure to follow.
Spieth has all the trappings of a future star, though the real measure will be over the course of a year instead of a month. Success at this level is all about consistency and learning how to cope with failure. There's still a long way to go.
"He's a great kid, obviously very mature," Leonard said. "I can't imagine being out there. I don't even know how old he is -- 19? I can't imagine being out here at 19 and to do what he's done. He hasn't just driven a couple hundred miles. He's been to three or four different countries this year already. It's pretty remarkable. It's beyond the game and what happens on the golf course. He's handling himself very, very well."
"At the beginning of the year, when you know that you only get seven unrestricted exemptions -- first of all, it's hard to get seven tournaments in, let alone make enough money to get your card -- to be able to do it in really three events ... I never would have guessed that I would get in this quickly," Spieth said. "I feel in control and I know what it's like to be in contention in a tour event. I just want to get back and get a win now."
He finished too late on Sunday to make his flight home to Dallas. He was still excited Sunday night, so instead of going to bed, he got together with his father, his caddie and his agent for a late-night game of poker. They didn't have poker chips, so they used M&Ms.

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RISE(UK)77mm Ultra Violet UV Protector Filter for Canon Nikon Samsung Sony Lens | eBay
Details about RISE(UK)77mm Ultra Violet UV Protector Filter for Canon Nikon Samsung Sony Lens
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Last updated on Jul 31, 2019 04:33:37 EDT View all revisions
Circular Size: 77mm To Fit: Camcorder, Camera
Brand: RISE UK Country/Region of Manufacture: China


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Prep DE gets in-home from Doba - Washington State - Scout
Prep DE gets in-home from DobaBARRY BOLTON01/18/2007WASHINGTON STATE head man Bill Doba was in the Southern California area yesterday out on the recruiting trail. One of the prospects he was there to see was prep defensive end Dominic Glover out of Mission Viejo, Calif., about 30 minutes south of Anaheim. The 6-4, 240-pounder is rated one of the top 50 prep defensive end prospects in the country, and he holds a WSU offer and visit date.Glover and Doba, along with d-ends coach Marty Long and area recruiting coach George Yarno, had a good visit on Wednesday, Glover said. "The head coach, the offensive line coach and the defensive line coach all came by. Yarno is an awesome guy, I like talking to him. It was a really good visit," said Glover.
Glover's official trip to Washington State is scheduled for a week from tomorrow. "I like Washington State a lot, I love the way that their defense plays. The school is cool, it's a cool college town, it's a really good environment," said Glover.
The Cougs were not the only ones getting some face time with Glover this week. Oregon and Oregon State have also stopped by, the Ducks on Monday and OSU on Wednesday.
"I actually just had a visit with Oregon State, it went really good. Oregon State brought their defensive line coach (Joe Seumalo) over. They answered a lot of questions my parents had about the school. My visit with them is for the 2nd, and my visit to Colorado is for this weekend."
Dominic Glover Share on Facebook Share on TwitterTrending on ScoutOregon 101: Regaining momentumKent: Expect more speed on WSU hardcourtWatch: NFL Top plays of Week 3Luani won’t be charged, but is damage done?The File on WSU's James WilliamsSee Pac-12 QB Commit in early senior action Full StoryCougfan Top StoriesOregon 101: Regaining momentumCALL IT a “first world problem” but Oregon has not lost consecutive games in a season since Mike Bellotti was their head coach. And Duck fans are not happy about it. Washington…by Matt MooreCougfan11:30 AMWSU hard after SDSU running back verbal?THREE-STAR running back prospect Chance Bell has put up some silly numbers thus far this season. Last week alone, the Burbank, Calif., product rushed for more than 300 yards and…by Braulio PerezCougfan9:20 AMKent: Expect more speed on WSU hardcourtERNIE KENT on Monday at Washington State’s on-campus media day said this year’s squad will speed things up more than last year. And he said the Cougs will be more intense on the…by the staff of Cougfan.comCougfan7:40 AMCFC TV: Slow starts? Falk thinks WSU’s solvedPULLMAN – Washington State starting quarterback Luke Falk says the Cougs really needed the bye week. Falk said the Cougs’ inability to start fast has been addressed, and that…by Skyler CracraftCougfanYesterday at 8:42 PMLuani won’t be charged, but is damage done?WHITMAN COUNTY PROSECUTOR Denis Tracy released a lengthy statement Monday, as reported by the Seattle Times, on why Cougar safety Shalom Luani won’t be charged in connection with…by the staff of Cougfan.comCougfanYesterday at 2:46 PMScout breaks down WSU verbal Connor NevilleWSU QUARTERBACK VERBAL Connor Neville is three games into his season season and has turned some heads with his performances. But what do the experts think? Scout.com National…by Greg BigginsScout FootballYesterday at 6:47 PMWhat Mike Leach said about Shalom LuaniPULLMAN – The majority of Mike Leach’s Monday press conference was overshadowed by one question. The Whitman County prosecutor released a statement on why he won’t be charging…by Skyler CracraftCougfanYesterday at 4:08 PMInside-outside: Is WSU where it wants to be?IN MIKE LEACH’s AIR RAID OFFENSE, the offense is crafted so that the outside receivers rack up more receiving yards than the inside receivers. The inside receivers, though, get…by Barry BoltonCougfanYesterday at 1:50 PMMoos: Everyone in Pac-12 is vulnerableBILL MOOS on Monday was struck by the strength, and parity, of the Pac-12 conference as Washington State prepares to enter conference play Saturday vs. Oregon (6:30 pm, Pac-12…by the staff of Cougfan.comCougfanYesterday at 12:48 PMThe File on WSU's James WilliamsTHE MAN WHO was No. 3 on the depth chart a month ago is now widely viewed as a prime component in Washington State's quest to reclaim a season off to an uncertain start.by Barry BoltonCougfanYesterday at 11:44 AMCommon thread in Cougar decommitments?WASHINGTON STATE has seen three recruiting decommitments in a week’s time, with safety Charles Watson, DT Lamonte McDougle and RB Cyrus Habibi-Likio all announcing they’d opened…by Barry BoltonCougfanYesterday at 10:45 AMNFL Cougar Highlights: Week ThreeTHE MUCH ANTICIPATED debut of Chris Ivory as a Jacksonville Jaguar was spoiled by a stingy Baltimore defense on Sunday, as the Ravens held the running back to just 14 yards on 12…by John C. WitterCougfanYesterday at 9:30 AMLoad More

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Home on Pinterest | 42 Pins
Kimberly (Ciptak) Saxon
42 Pins 68 Followers Follow Board
Where the heart is Home | cottage |
2 | bathrooms
These are the colors Im doing my living room in in a month or so, so tired of brown cream and orange.
Beautiful front entrance with slate stone walkway and porch, solar lighting and landscaping that works year-round.
grasscloth + beadboard
I love these chairs - this is exactly what I want to do in my dining room
White furniture and paper lantern, with natural wicker chairs for contrast, and of course green foliage for freshness.
60% OFF Blissliving Home Nirvana Coverlet Set (Storm Grey)
mantle flowers with all white room
These polkadots are in Haven's baby bedding, I would love to convert her room to a big girl room like this!
I love the colors of this bedroom and I like how they out the green blanket on the pink chair!
if you couldn't tell already, i'm a sucker for the pink/green combo!
Antiqued Teal Green Chest of Drawers by Artisan8 on Etsy
could also paint a tree with hooks to hang necklaces and bracelets on!
insidetheframedesign.blogspot.com
Small changes you can make to create a mantel masterpiece! How to Decorate a Mantel | SAS Interiors
-painted the walls (Behr Porpoise and Behr Creek Bend for the accent wall) -stenciled one wall using a homemade stencil and pearlescent craft paint -recovered lampshades with muslin and ribbon
I love this gray quatrefoil pattern on the wall...with the yellow of course. LOVE.
shabby chic nostalgic farmhouse. pretty.
Love the white and gray walls with a touch of color accent.
Revive an old piece of furniture with a fresh coat of paint. Try a look-at-me shade, like turquoise, citrus yellow, lacquer red or apple green to draw attention to a vintage piece's lines. Design by Rate My Space user fleamarkettrixie
Custom Craftsman Orange County Interior Design Hallway, via Flickr.
Entry way - so inviting.
@Raynel Knight I think that lampshade you liked is covered in fabric. You should be able to recover one in a print that you like. This one looks redone too, though I didn't find directions. I bet there's a tutorial onlien.
Love Everything but the chair color- I would prolly go with a crazy teal and paint the rest of my walls grey
Nice, soft colors
Grey room with a pop of yellow/gold!


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9780077352233: Emergency Medical Responder: The Workbook - AbeBooks - Aehlert, Barbara: 0077352238
Emergency Medical Responder: The Workbook
ISBN 13: 9780077352233
Publisher: McGraw-Hill Science/Engineering/Math, 2010 ISBN 10: 0077352238
1. Emergency Medical Responder: The Workbook
ISBN 10: 0077352238
Book Description McGraw-Hill Education. Book Condition: New. Brand New Item, Never Used! Fast Shipping! **RECEIVE IN 2-3 BUSINESS DAYS WHEN YOU CHOOSE EXPEDITED SHIPPING!** Still in original plastic. Expedited shipping 2-3 business days; Standard shipping 2-14 business days. Ships with delivery confirmation. Bookseller Inventory # ANK-4H1-0179
2. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Science/Engineering/Math, 2010. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Barbara Aehlert is the President of Southwest EMS Education, Inc. in Phoenix, Arizona and Pursley, Texas. She has been a registered nurse for more than 30 years with clinical experience in medical/surgical and critical care nursing and, for the past 18 years, in prehospital education. Barbara is an active CPR, First Aid, ACLS, and PALS instructor and takes a special interest in teaching basic dysrhythmia recognition to nurses and paramedics. She is a consultant with the Southwest Ambulance paramedic program in Mesa, Arizona, and an active member of the Pursley, Texas, Volunteer Fire Department. Bookseller Inventory # ABE_book_new_0077352238
3. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Education. PAPERBACK. Book Condition: New. 0077352238 Premium - Never used in classroom. Bookseller Inventory # P5034616
4. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Science/Engineering/Math, 2010. Paperback. Book Condition: New. book. Bookseller Inventory # 0077352238
5. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Education, 2010. Paperback. Book Condition: New. Bookseller Inventory # P110077352238
6. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Education. PAPERBACK. Book Condition: New. 0077352238 New Condition. Bookseller Inventory # NEW4.0035815
7. Emergency Medical Responder: The Workbook
Book Description McGraw-Hill Science/Engineering/Math, 2010. Paperback. Book Condition: New. 2. Bookseller Inventory # DADAX0077352238
8. Emergency Medical Responder (Paperback)
Book Description 2010. Paperback. Book Condition: New. 2nd. 215mm x 276mm x 12mm. Paperback. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 320 pages. 0.637. Bookseller Inventory # 9780077352233
9. Emergency Medical Responder: The Workbook Format: Softcover
Book Description Mcgraw Hill Publishers. Book Condition: New. Brand New. Bookseller Inventory # 0077352238
10. Emergency Medical Responder (Paperback)
Book Description 2010. Paperback. Book Condition: New. 2nd. 215mm x 276mm x 12mm. Paperback. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 320 pages. 0.637. Bookseller Inventory # 9780077352233

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(Redirected from Linear B script)
Linear B is a syllabic script that was used for writing Mycenaean Greek, the earliest attested form of Greek. The script predates the Greek alphabet by several centuries. The oldest Mycenaean writing dates to about 1450 BC.[1] It is descended from the older Linear A, an undeciphered earlier script used for writing the Minoan language, as is the later Cypriot syllabary, which also recorded Greek. Linear B, found mainly in the palace archives at Knossos, Cydonia,[2] Pylos, Thebes and Mycenae,[3] disappeared with the fall of Mycenaean civilization during the Bronze Age Collapse. The succeeding period, known as the Greek Dark Ages, provides no evidence of the use of writing. It is also the only one of the three "Linears" (the third being Linear C, aka Cypro-Minoan 1) to be deciphered, by English architect and self-taught linguist, Michael Ventris.[4]

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Words containing eudocollo | Words that contain eudocollo
Words containing eudocollo | Words that contain eudocollo http://www.thefreedictionary.com/words-containing-eudocolloPrinter Friendly
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Found 1 words containing eudocollo. Browse our Scrabble Word Finder, Words With Friends cheat dictionary, and WordHub word solver to find words that contain eudocollo. Or use our Unscramble word solver to find your best possible play!
13 letter words containing eudocolloSee also13 letter words containing eudocollopseudocolloidSee also:8-letter wordsWords that start with cWords that start with nWords that end in jWords that start with yWords that end in ingWords containing eudocollWords containing eudocolloiWords containing eudocollu

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Does God Need Our Help?: Cloning, Assisted Suicide, & Other Challenges in Bioethics by John Frederic Kilner, PH.D., C Ben Mitchell, Dan Taylor (Editor) - New, Rare & Used Books Online at Alibris Marketplace
Does God Need Our Help?: Cloning, Assisted Suicide, & Other Challenges in Bioethics	by
John Frederic Kilner, PH.D., C Ben Mitchell, Dan Taylor (Editor)
The authors spark discussion and debate on the Bible's words about genetic cloning.
Does God Need Our Help?: Cloning, Assisted Suicide, & Other Challenges in Bioethics – Hardcover
by John Frederic Kilner, PH.D., C Ben Mitchell, Dan Taylor (Editor)
ISBN: 0842374469
ISBN-13: 9780842374460
John Frederic Kilner, PH.D. (Editor), Judy Allen Shelly (Editor), Judith A Shelly (Editor)
Title: Does God Need Our Help
John Frederic Kilner, PH.D., C Ben Mitchell
9780842374460
Title: Does God Need Our Help? : Cloning, Assisted Suicide, & Other Challenges. (Vital Questions)
Title: Does God Need Our Help?: Cloning, Assisted Suicide, & Other Challenges in Bioethics
Fair. Our feedback rating says it all: Five star service and fast delivery! We have shipped four million items to happy customers, and have one MILLION unique items ready to ship today! v. Glued binding. Paper over boards. 236 p. Vital Questions.
Description: Fair. Glued binding. Paper over boards. 236 p. Vital Questions.
Fair. Glued binding. Paper over boards. 236 p. Vital Questions.
Title: Does God Need Our Help? : Cloning, Assisted Suicide, & Other Challenges in Bioethics
Publisher: The Center for Bioethics
Description: pp. 236. Hardcover, no dust jacket. VG. This is located at our...
pp. 236. Hardcover, no dust jacket. VG. This is located at our store in Portland, Oregon; please anticipate extra delivery time.
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text: View: Play-By-Play | Pitch-By-PitchInning: All | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9Pittsburgh - Top of 4thSCOREBrooks Raley pitching for ChicagoPITCHCJosh HarrisonBall, Strike (looking), Strike (foul), Ball, Strike (swinging), J Harrison struck out swinging41Gerrit ColeBall, Strike (looking), Strike (foul), Foul, Foul, Ball, Strike (swinging), G Cole struck out swinging41Starling MarteS Marte singled to center41Jordy MercerBall, J Mercer lined out to right410 Runs, 1 Hits, 0 ErrorsChicago - Bottom of 4thSCOREGerrit Cole pitching for PittsburghPITCHCAnthony RizzoA Rizzo grounded out to shortstop41Dioner NavarroBall, Strike (swinging), D Navarro grounded out to second41Nate SchierholtzStrike (looking), N Schierholtz fouled out to third410 Runs, 0 Hits, 0 Errors


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Frank M Flanagan Books New, Rare & Used Books - Alibris
Frank M. Flanagan currently teaches in the School of Art and Design at the Limerick Instutite of Technology, Ireland, having retired from his position as Senior Lecturer in Education at Mary Immaculate College, University of Limerick, Ireland.
Frank M. Flanagan currently teaches in the School of Art and Design at the Limerick Instutite of Technology, Ireland, having retired from his position as Senior Lecturer in Education at Mary Immaculate College, University of Limerick, Ireland. See less
Frank M Flanagan book subjects
Frank M Flanagan's Featured Books
Confucius, the Analects, and...
Confucius, the Analects and...


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ABC of Getting the MBA Admissions Edge (Us): Officially Supported by McKinsey Co. and Goldman Sachs book by Matt Symonds, Alan Mendonca | 1 available editions | Alibris Books
Getting into MBA programs is more and more competitive. This over 600 page book will improve your chances of admission to the schools of your choice. This version of The Edge, aimed at US applicants, features an in-depth analysis of applying to each schoo Read More
Getting into MBA programs is more and more competitive. This over 600 page book will improve your chances of admission to the schools of your choice. This version of The Edge, aimed at US applicants, features an in-depth analysis of applying to each schoo Read Less
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Alibris ID: 14025517639
This is an ex-library book and may have the usual library/used-book markings inside. This book has soft covers. In good all round condition., 1100grams, ISBN: 9780971482203.
Alibris ID: 14054414362
Very Good. 0971482209 creased cover.
Alibris ID: 13120251820
$34.48 $49.00
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Alibris ID: 12585389011
Books by Matt Symonds


text:
Marble (3,687)
Granite (3,371)
Engineered Quartz (2,542)
Solid Surface (1,163)
Tile Color White (69)
Tile Material Ceramic Tile (112)
Sink Drop-in (108)
Find out if your remodeling dreams fit your budget reality.Try the Real Cost Finder 242 wall fence Bath Design Photos
Ideabooks18,752	Questions18	built in bench and display shelving. .
Flooring, wall surfaces, tile selections Lighting design, fixture selections & controlsLove the wall art. Where can I find them to purchase?Who makes the lights over the art on back wall?Beautiful room and Nice tilework on the wall! Are they cut to size?original post concerning the wall "tile'? I located one from Nov '13, but not the original. More questions concerning the wall. What weight of buildersyou can move on to finish selections of trim details, flooring, wall surfaces (planks, wall paper, or just paint), cabinetry color, counter tops, etc. ThisHello Art, I had done a post on this before, but the tile on the walls is actually wood. It is clear pine with several coats of quality primer andLarge mirror and sink storage units — maggieclifford Embed
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Ideabooks5,529	Questions7	Back wall shelf in shower on side wall of showerGrey walls, white tub, sink, wood (looking?) floor.Hole in the shower wall for batles...Shelf on one wall...Bathtub against the wall...Hole in wall...The openings of the wall...Wall ColorTile color — Jedanna Owens Embed
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Patent US5257218 - Parallel carry and carry propagation generator apparatus for use with carry ... - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inAdvanced Patent SearchPatentsA parallel carry and carry propagation generator for use with a modulo-2 N-bit operand adder generates the required carry bits to complete the N-bit pair modulo-2 sums as a parallel operation. The logic structure has log.sub.2 2N operation levels that allow for constant fan-in and fan-out design as well...http://www.google.com/patents/US5257218?utm_source=gb-gplus-sharePatent US5257218 - Parallel carry and carry propagation generator apparatus for use with carry-look-ahead addersAdvanced Patent SearchPublication numberUS5257218 APublication typeGrantApplication numberUS 08/013,256Publication dateOct 26, 1993Filing dateFeb 3, 1993Priority dateJan 6, 1992Fee statusPaidPublication number013256, 08013256, US 5257218 A, US 5257218A, US-A-5257218, US5257218 A, US5257218AInventorsJack T. PoonOriginal AssigneeIntel CorporationExport CitationBiBTeX, EndNote, RefManPatent Citations (5), Non-Patent Citations (2), Referenced by (26), Classifications (10), Legal Events (3) External Links: USPTO, USPTO Assignment, EspacenetParallel carry and carry propagation generator apparatus for use with carry-look-ahead addersUS 5257218 AAbstract A parallel carry and carry propagation generator for use with a modulo-2 N-bit operand adder generates the required carry bits to complete the N-bit pair modulo-2 sums as a parallel operation. The logic structure has log.sub.2 2N operation levels that allow for constant fan-in and fan-out design as well as static, rather than fixed-rate precharge/discharge, operation. A simplified version of the network is also suitable for use as a conditional sum selection controller for a conditional sum adder.
What is claimed is: 1. An N-bit two operand carry generator logic array operating on corresponding operand bit pairs comprising:(a) a zero level (I=0) multiplicity of N gates in parallel for the logical AND-ing of the corresponding operand bit pairs producing at each gate output the carry term associated with the operand input bit pairs, said gate outputs being arranged in ascending order corresponding to the ascending order of significance of the operand input bit pairs; (b) a carry generator processor having a first, second and third input, said first and second inputs connected to distinct partial carry terms of the next lower level and said third input connected to an associated propagation carry term provided by a carry propagation generator for producing at the processor output a next level partial carry input term; (c) a first level (I=1) multiplicity of N-1 carry generator processors arranged in ascending order of significance, each processor having a first, second and third input, each said first input connected to one corresponding zero level gate output for all said N gate outputs except that associated with the least significant of the input bit pairs, said second input of each processor connected to the output of the zero level gate associated with the next lower significant operand bit pairs, each said third processor input connected to the corresponding zero level output of a carry propagation generator, producing at each processor output a partial first level carry term arranged in ascending order; and (d) additional higher levels (I=2, 3, . . . , L) of carry generator processors, each level having N-2.sup.I-1 processors with each said first carry generator processor input connected to one corresponding next lower level carry generator processor output for all outputs in ascending order beginning at the 2.sup.I-1 output, said second input of each processor connected to the output of the next lower level processor at 2.sup.I-1 positions below the corresponding next lower level processor input to said first input, and said third processor input connected to a corresponding I.sup.th level carry propagation generator output. 2. An N-bit carry generator logic array as in claim 1 wherein said carry generator processor comprises:(a) an OR-gate with an output and a first and second input, said first input connected to said processor first input, said OR-gate output being said processor output; and (b) an AND-gate with its output connected to said OR-gate second input, with a first and second input, said first input connected to said processor second input, and said second AND-gate input connected to said processor third input. 3. A carry generating network for N-bit operands comprising:(a) an N-bit two operand carry generator logic array operating on corresponding operand bit pairs comprising:(i) a zero level (I=0) multiplicity of N gates in parallel for the logical AND-ing of the corresponding operand bit pairs producing at each gate output the carry term associated with the operand input bit pairs, said gate outputs being arranged in ascending order corresponding to the ascending order of significance of the operand input bit pairs; (ii) a carry generator processor having a first, second and third input, said first and second inputs connected to distinct partial carry terms of the next lower level and said first and said third input connected to an associated propagation carry term provided by a carry propagation generator for producing at the processor output a next level partial carry input term; (iii) a first level (I-1) multiplicity of N-1 carry generator processors arranged in ascending order of significance, each processor having a first, second and third input, each said first input connected to one corresponding zero level gate output for all said N gate outputs except that associated with the least significant of the input bit pairs, said second input of each processor connected to the output of the zero level gate associated with the next lower significant operand bit pairs, each said third processor input connected to the corresponding zero level output of an N-bit carry propagation generator, producing at each processor output a partial first level carry term arranged in ascending order; and (iv) additional higher levels (I=2,3, . . . L) of carry generator processors, each level having N-2.sup.I-1 processors with each said first carry generator processor input connected to one corresponding next lower level carry generator processor output for all outputs in ascending order beginning at the 2.sup.I-1 output, said second input of each processor connected to the output of the next lower level processor at 2.sup.I-1 positions below the corresponding next lower level processor input to said first input, and said third processor input connected to a corresponding I.sup.th level N-bit carry propagation generator output; and (b) an N-bit carry propagation generator for providing multilevel ordered propagation terms to said carry generator, with multiple level output propagation terms, and its outputs connected to corresponding same level carry generator processors. 4. A carry generating network as in claim 3 wherein said N-bit carry propagation generator further comprises:(a) a zero level (I=0) multiplicity of N-1 gates for the logical OR-ing of the two operand corresponding bit pairs for all bit pairs except the least significant, producing at each gate output, its associated first level conditional carry term arranged in ascending order of the operand bit pair inputs; (b) a first level (I=1) multiplicity of N-2 AND-gates, each said gate accepting as inputs adjacent overlapping ascending order outputs producing an ordered ascending set of second level conditional carry terms; and (c) additional higher levels of AND-gates, each succeeding level having N-2.sup.I AND-gates, each said gates having a first input connected its corresponding lower level ordered output and second input connected to the 2.sup.Ith lesser ordered output of said lower level, for forming the required higher level up to and including level, I=L, for which 2.sup.I =N/2; each level producing succeeding higher order conditional carry terms at the individual AND-gate outputs. 5. A carry-look-ahead modular adder network comprising:(a) a modular adder unit comprising:(i) input means for accepting two N-bit operands and a carry-in bit; (ii) a conditional sum adder connected to said input means for forming two conditional operand sums based on the two possible states of the carry-in bit; and (iii) a carry generating network with its input connected to said input means for generating a carry-out bit from the two operands and carry-in bit, said carry generating network comprising:an N-bit two operand carry generator logic array operating on corresponding operand bit pairs comprising; a zero level (I=0) multiplicity of N gates in parallel for the logical AND-ing of the corresponding operand bit pairs producing at each gate output the carry term associated with the operand input bit pairs, said gate outputs being arranged in ascending order corresponding to the ascending order of significance of the operand input bit pairs; a carry generator processor having a first, second and third input, said first and second inputs connected to distinct partial carry terms of the next lower level and said first and said third input connected to an associated propagation carry term provided by a carry propagation generator for producing at the processor output a next level partial carry input term; a first level (I-1) multiplicity of N-1 carry generator processors arranged in ascending order of significance, each processor having a first, second and third input, each said first input connected to one corresponding zero level gate output for all said N gate outputs except that associated with the least significant of the input bit pairs, said second input of each processor connected to the output of the zero level gate associated with the next lower significant operand bit pairs, each said third processor input connected to the corresponding zero level output of an N-bit carry propagation generator, producing at each processor output a partial first level carry term arranged in ascending order; additional higher levels (I=2,3, . . . L) of carry generator processors, each level having N-2.sup.I-1 processors with each said first carry generator processor input connected to one corresponding next lower level carry generator processor output for all outputs in ascending order beginning at the 2.sup.I-1 output, said second input of each processor connected to the output of the next lower level processor at 2.sup.I-1 positions below the corresponding next lower level processor input to said first input, and said third processor input connected to a corresponding I.sup.th level N-bit carry propagation generator output; and an N-bit carry propagation generator for providing multilevel ordered propagation terms to said carry generator, with multiple level output propagation terms, and its outputs connected to corresponding same level carry generator processors; and (b) a multiplicity of said modular adder units connected in tandem in ascending order of significance so that the operand bit fields are partitioned into corresponding non-overlapping operand subfields, each subfield of increasing significance being assigned to the tandem modular adder units in ascending order of significance so that the sum from each modular adder is a corresponding subfield of the operand sum and the carry-in bit to each modular adder unit is the carry-out bit of the previous modular adder unit. 6. A carry-look-ahead modular adder network comprising:(a) input means for accepting two N-bit operands; (b) a multiplicity of N one-bit conditional sum adders, each having a sum select input, each connected to the input means to a distinct pair of corresponding bits of the two operands for forming a conditional sum of each corresponding operand bit pairs ordered in ascending significance; and (c) a carry generating network operating on the two N-bit operands, for generating at its output a multibit field or ordered carry-bits, ordered to correspond to the conditional sum select input bit of said conditional sum adders, each succeeding higher order carry generator output bit connected to the succeeding sum select input of said multiplicity of ordered one-bit conditional adders thereby producing at the output of the ordered conditional sum adders a field of bits corresponding to the sum of the two N-bit operands, said carry generating network comprising;an N-bit two operand carry generator logic array operating on corresponding operand bit pairs comprising; a zero level (I=0) multiplicity of N gates in parallel for the logical AND-ing of the corresponding operand bit pairs producing at each gate output the carry term associated with the operand input bit pairs, said gate outputs being arranged in ascending order corresponding to the ascending order of significance of the operand input bit pairs; a carry generator processor having a first, second and third input, said first and second inputs connected to distinct partial carry terms of the next lower level and said first and said third input connected to an associated propagation carry term provided by a carry propagation generator for producing at the processor output a next level partial carry input term; a first level (I-1) multiplicity of N-1 carry generator processors arranged in ascending order of significance, each processor having a first, second and third input, each said first input connected to one corresponding zero level gate output for all said N gate outputs except that associated with the least significant of the input bit pairs, said second input of each processor connected to the output of the zero level gate associated with the next lower significant operand bit pairs, each said third processor input connected to the corresponding zero level output of an N-bit carry propagation generator, producing at each processor output a partial first level carry term arranged in ascending order; additional higher levels (I=2, 3, . . . L) of carry generator processors, each level having N-2.sup.I-1 processors with each said first carry generator processor input connected to one corresponding next lower level carry generator processor output for all outputs in ascending order beginning at the 2.sup.I-1 output, said second input of each processor connected to the output of the next lower level processor at 2.sup.I-1 positions below the corresponding next lower level processor input to said first input, and said third processor input connected to a corresponding I.sup.th level N-bit carry propagation generator output; and an N-bit carry propagation generator for providing multilevel ordered propagation terms to said carry generator, with multiple level output propagation terms, and its outputs connected to corresponding same level carry generator processors. 7. A carry-look-ahead modular adder as in claim 6 wherein each of the one-bit conditional sum adders comprises:(a) a first exclusive-or network connected to an operand bit pair of said input means for forming the modulo-2 sum of corresponding bit pairs of the two operands at its output that is representative of the first conditional sum; and (b) a second exclusive-or network with an output, and a first and second input, the first input connected to the output of said first exclusive-or network, the second input connected to the corresponding carry generator output bit for use as a carry-in conditional sum select bit by forming the complement of said first exclusive-or first conditional sum which is representative of the second conditional sum and selecting the appropriate sum as determined by the state of the carry-in bit, the output being representative of the sum of the two operand bits and the carry-in bit. 8. A carry-look-ahead modular adder as in claim 6 wherein said input means further comprises means for accepting a least significant carry-in bit and connecting the carry-in bit to the carry-in sum select input of the least significant one-bit conditional adder.
10. A simplified N-bit operand carry generator logic array for use with carry-look-ahead conditional sum adders with a carry-in, comprising:(a) a carry propagation generator for generating carry propagation terms from the two N-bit operands and an input carry; (b) a zero-level (I=0) multiplicity of N gates in parallel for the logical AND-ing of corresponding operand bit pairs producing at each gate output the carry term associated with the corresponding input operand bit pair, the N outputs being arranged in ascending order (0, 1, 2, . . . , N-1) corresponding to the ascending order of the associated operand bit pairs; (c) a carry generator processor having a first, second and third input, said first and second inputs connected to distinct partial carry terms of the next lower level and said third input connected to an associated propagation carry term provided by a carry propagation generator for producing at its output a next level partial carry input term; (d) a first level (I=1) multiplicity of N/2 carry generator processors arranged in ascending order of significance, each first input of said processors connected to one odd order (n=1, 3, 5, . . . , N-1) gate output, each second input of said processors connected to the output of the zero level gate associated with the next least significant gate output (0, 2, 4, . . . , N-2), each third input of said processors connected to the corresponding zero level output of said carry propagation generator, producing at each processor output a partial carry term of second order arranged in ascending order; (e) additional higher levels (I=2, 3, L=log.sub.2 N, . . . , L) of carry generator processors, each level up to L=log.sub.2 N having 2.sup.-I N carry generator processors with each first input connected to one corresponding next lower level processor output, each second input connected to the output of the next lower level processor at 2.sup.I-1 positions below the corresponding next lower level processor, and the third input connected to the corresponding I.sup.th level carry propagation generator output; and (f) a final, highest level (I=L+1) comprising a single carry generator processor with the first input connected to the output of the next lower level processor, the second processor input connected to the carry-in bit, and the third processor input connected to the corresponding L+1 level carry propagation output term, thereby producing a single output carry bit corresponding to the output carry resulting from the sum of the two operands and the carry-in bit. 11. A two level carry generating module for generating two levels (I=m, m+1) of carry generator terms, comprising:(a) a first set of input terminals for accepting corresponding m-1 level partial carry output terms; (b) a second set of input terminals for accepting associated displaced m-1 level partial carry output terms; (c) a third set of input terminals for accepting associated m level propagation carry terms; (d) a fourth set of input terminals for accepting associated displaced m level partial carry output terms; (e) a fifth set of input terminals for accepting associated m+1 level propagation carry terms; (f) a first set of output terminals for outputting the m level partial carry terms; (g) a second set of output terminals for outputting the (m+1) level partial carry terms; (h) a carry generator processor comprising:i) an OR-gate with an output and a first and second input, said first input connected said processor first input, said OR-gate output being said processor output; ii) an AND-gate with its output connected to said OR-gate second input, with a first and second input, said first input connected to said processor second input, and said second AND-gate input connected to said processor third input; (i) a multiplicity of said carry generator processors comprising an m level set of processors, said first input of each processor connected to a corresponding terminal of said first set of input terminals, said second input of each processor connected to a corresponding terminal of said second set of input terminals, and said third input of each processor connected to a corresponding terminal of said third set of input terminals, said output of each processor connected to a corresponding terminal of said first set of output terminals; and (j) a multiplicity of said carry generator processors comprising an (m+1) level set of processors, said first input of each processor connected to the output of a distinct corresponding m-1 level processor, said second input of each processor connected to a corresponding terminal of said fourth set of input terminals, said third input of each processor connected to a corresponding terminal of said fourth set of input terminals, said third input of each processor connected to a corresponding terminal of said fifth set of input terminals, said output terminal of each processor connected to a corresponding output of said second set of output terminals. Description
Early digital computers used ripple-carry adders in which the i.sup.th adder output bit may be represented by the modulo-2 bit sum
S.sub.i =A.sub.i ⊕B.sub.i ⊕C.sub.i-1
where A.sub.i and B.sub.i are the i.sup.th bit of the input operands, and C.sub.i-1 is the carry-in from the next lowest bit sum. The carry-in may be represented in terms of the prior stage operands (A.sub.i-1, B.sub.i-1) and the prior stage carry-in, C.sub.i-2, as C.sub.i-1 =A.sub.i-1 *B.sub.i-1 +C.sub.i-2 (A.sub.i-1 +B.sub.i-1) where (*,+) are Boolean (AND, OR) operators respectively. The time for the carry-bits to ripple through became the limiting factor in the speed of adders. Subsequent fixed-time adders were introduced to overcome these deficiencies. These fixed-time adders may be classified into two categories: conditional sum and carry-look-ahead (CLA) adders.
Conditional adders compute each bit sum, S.sub.i, twice: one sum, S.sub.Ni, based on the assumption that the carry-in bit, C.sub.i, is zero; a second sum, S.sub.Ei, on the assumption that C.sub.i =1. FIG. 1 is the logic diagram of a 4-bit-slice conditional sum adder. (Ref. "Introduction to Arithmetic", Waser and Flynn, Holt, Rinehart and Winston, 1982, p. 77ff). The two input operands are represented by input bits A.sub.0, A.sub.1, A.sub.2, A.sub.3 and B.sub.0, B.sub.1, B.sub.2, B.sub.3, respectively. Each pair of operand bits (A.sub.i, B.sub.i) are applied to input terminals 110. A.sub.0, B.sub.0 correspond to the input operand least significant bit while A.sub.3, B.sub.3 correspond to the most significant bits. The conditional sum adder consists of two basic sections: the conditional sum generator unit 130 that forms at its output the two sets of conditional sums and conditional carry, S.sub.N0, S.sub.N1, S.sub.N2, S.sub.N3, C.sub.N4 and S.sub.E0, S.sub.E1, S.sub.E2, S.sub.E3, C.sub.E4, the latter group being based on the assumption of a non-zero carry-in to its corresponding individual conditional sum generator 141, 143, 145, 147, 149, respectively. These conditional signals are applied to conditional sum selector unit 150 consisting of the individual output selectors 161, 163, 165, 167, 169 corresponding to output sum bits S.sub.0, S.sub.1, S.sub.2, S.sub.3 and output carry bit C4. The selection is controlled by the carry-in bit, C.sub.0, and its complement, C.sub.0, operating on the conditional sums by means of AND-gates 113 and OR-gates 115.
S.sub.N0 =A.sub.0 ⊕B.sub.0
S.sub.N1 =A.sub.1 ⊕B.sub.1 ⊕G.sub.0
S.sub.E1 =A.sub.1 ⊕B.sub.1 ⊕P.sub.0
S.sub.N2 =A.sub.2 ⊕B.sub.2 ⊕(G.sub.1 +T.sub.1 G.sub.0)
S.sub.E2 =A.sub.2 ⊕B.sub.2 ⊕(G.sub.1 +T.sub.1 P.sub.0)
S.sub.N3 =A.sub.3 ⊕B.sub.3 ⊕(G.sub.2 +T.sub.2 G.sub.1 +T.sub.2 T.sub.1 G.sub.0)
S.sub.E3 =A.sub.3 ⊕B.sub.3 ⊕(G.sub.2 +T.sub.2 G.sub.1 +T.sub.2 T.sub.1 P.sub.0)
P.sub.i =A.sub.i B.sub.i,
T.sub.i =A.sub.i ⊕B.sub.i.
S.sub.i =A.sub.i ⊕B.sub.i ⊕C.sub.i-1,  i=0, 1, 2, 3
The above CLA sum expression can be immediately evaluated, absent the carry term (C.sub.i-1), by forming the EOR of the two operands (A.sub.i, B.sub.i). The carry term, C.sub.i-1, is a function of lower order indexed operands, (A.sub.i-1, B.sub.i-1), and lower order carries, C.sub.i-2. As a result, the time to complete an addition is generally governed by availability of the carry-in bit to each sum-bit.
The above expression for C.sub.i is a recursive equation, i.e., one in which the current value, C.sub.i+1, is a function of its own past values. It may be explicitly stated as follows:
and P.sub.0 '=P.sub.3 P.sub.2 P.sub.1 P.sub.0 C.sub.0 obtains C.sub.4 =G.sub.0 '+P.sub.0 'C.sub.0 which represents the logical expression for the G.sub.0 ',P.sub.0 ' output terminals of FIG. 2.
where G'.sub.1 and P'.sub.1 are the CLA output pair of the next higher order CLA modular unit.
Modularity was extended by means of a four group CLA generator that accommodated four CLA 4-bit slice adders and produced at output the necessary carry information, i.e., C.sub.4, C.sub.8, C.sub.12 and P", G", to form a 16-bit CLA adder using four modular adder units of the type shown in FIG. 2. FIG. 3 shows a four group CLA generator with four input pairs, (G'.sub.0,P'.sub.0), (G'.sub.1,P'.sub.1), (G'.sub.2,P'.sub.2) and (G'.sub.3,P'.sub.3) and carry outputs corresponding to C.sub.4, C.sub.8, C.sub.12 and (P", G"), where
FIG. 4 shows the logical extension of modular CLA concept to 64-bit addition. A total of sixteen modular 4-bit slice SLA adders 200 are arrayed in parallel to accept input operand pairs, (A.sub.0, B.sub.0) . . . (A.sub.3, B.sub.3), (A.sub.4, B.sub.4) . . . (A.sub.7, B.sub.7), . . . , (A.sub.60, B.sub.60) . . . (A.sub.63, B.sub.63) and carry-in bits, (C.sub.0, C.sub.16, C.sub.32, C.sub.48), each producing 4-bit output sums, (S.sub.0, S.sub.1, S.sub.3) . . . (S.sub.60, S.sub.61, S.sub.62, S.sub.63) and carry-generate/carry-propagate pairs (P'.sub.0,G'.sub.0), . . . (P'.sub.15,G'.sub.15).
A second logical level of four modular four group CLA generators 250, each accepting the carry output information of a corresponding group of four CLA adders 200, generates the necessary carry information for its associated adders 200 from the four pairs of carry-generate/carry-propagate pairs and the necessary carry-generate/carry-propagate pairs, [(P".sub.0,G".sub.0), (P".sub.1,G".sub.1), and (P".sub.2,G".sub.2)], from which the third logic level consisting of a single CLA generator 250 generates the three additional carry-in bits, (C.sub.16, C.sub.32, C.sub.48) supplied to the first and second levels. In this manner, modular 4-bit slice CLA adders have been used to accommodate higher precision operation.
Because the logic required to implement the above expressions is identical to that of the CLA generator 250 of FIG. 3 and 4, a 16-bit adder may be implemented as shown in FIG. 5. The adder has four conditional adders 100 connected in parallel, each accepting 4-bit pairs of operands. Each adder 100 consists of a conditional sum generator 130 and a multiplexor 150. The modular group carry-out pairs, [(C.sub.N4, C.sub.E4), (C.sub.N8, C.sub.E8), (C.sub.N12, C.sub.E12)], are supplied to CLA generator 250 which produces the modular carry-in bits (C4, C8, C12) required to form the sixteen bit addition. The extension required to accommodate more bits clearly indicated by the CLA method previously discussed.
SUMMARY OF THE INVENTION A parallel N-bit binary adder network is described comprising a multiplicity of parallel modulo-2 adders, each accepting and summing corresponding operand bit pairs and a final sum carry input. The final sum carry bits are generated in parallel by a carry generating network that comprises a parallel carry propagation logic array for generating carry propagation terms based on the logical OR-ing of pairs of input operand bits, a carry generation logic network based on AND-ing of pairs of input operand bits, and a logic array for operating on the carry generating and propagation terms, in parallel for producing a set of final sum carry terms that are fed in parallel to the modulo-2 parallel adders, or by using the most significant carry bit for selecting one of two sums in a conditional sum adder. The number of gate delays for generating the final set of N sum carry inputs to the modulo-2 adder is [log.sub.2 2N], providing a substantial increase in adder throughput.
represents the value of the i.sub.th sum bit expressed as the modulo-2 sum of the i.sup.th operand bit values (Ai, Bi) and the carry-in bit Ci-1, from the modulo-2 sum of the next least significant bit pair (A.sub.i-1, B.sub.i-1). Thus, by using the boolean logic operators (*) for "AND" and (+) for "OR", the carry bits may be expressed as ##EQU1##
so that the above carry bit expression become ##EQU2## (Note that for further convenience, the explicit "AND" operator symbol has been omitted so that P.sub.i C.sub.i ≡P.sub.i * C.sub.i). This convention will be used throughout the following description.
Thus, g=[G.sub.0 G.sub.1 G.sub.2 . . . G.sub.N-1 ].sup.T =[A.sub.0 B.sub.0 A.sub.1 B.sub.1 A.sub.2 B.sub.2 . . . A.sub.N-1 B.sub.N-1 ].sup.T represents the "AND"-ing of operand bit pairs which generate a carry-out when high. Matrix P, whose elements represent propagation control variables, describes the means by which the carry-outs are propagated to and through higher order bits.
Thus, at each binary increment, 2.sup.k ≦r<2.sup.k+1, P.sup.(r) is factorizable into (k+1) lower triangle matrices of the form shown. These factorized equations may be represented by the flow diagrams of FIGS. 6, 7 and 8.
FIG. 6 corresponds to the four-bit carry generation process represented by the factorization of P.sup.(4). The input to the process consists of the carry-generator vector, [G.sub.0 G.sub.1 G.sub.2 G.sub.3 ].sup.T shown at the bottom. The diagonal lines with arrow-heads correspond to multiple ("AND") operations on the data of the node of origin by the corresponding labelled expression. Unlabeled vertical lines between nodes represent transmission paths with no modification of data transmitted from a lower node to a higher node. All nodes are summing ("OR") junctions. For example, C.sub.1 =G.sub.1 +P.sub.1 G.sub.0 and C.sub.3 =P.sub.3 P.sub.2 (G.sub.1 +P.sub.1 G.sub.0)+(G.sub.3 +P.sub.3 G.sub.2)=P.sub.3 P.sub.2 P.sub.1 G.sub.0 +P.sub.3 P.sub.2 G.sub.1 +P.sub.3 G.sub.2 +G.sub.3. The carry-out vector, [C.sub.0 C.sub.1 C.sub.2 C.sub.3 ].sup.T, is represented by the values present at the upper output nodes.
For each binary increment, 2.sup.k ≦r≦2.sup.k+1 -1, or for each doubling of the number of bits used in the operands, one additional sparse lower triangular matrix is required to represent the factorized form of the P.sup.(r) matrix. Thus, for 2≦r≦3, P.sup.(r) factors into 2 matrices; for 4≦r≦7, P.sup.(r) factors into 3 matrices, and for 2.sup.k ≦r≦2.sup.k+1 -1, P.sup.(r) factors into (k+1) matrices.
In general, k+1 factorized matrices (stages) are required for 2.sup.k+1 bits in each operand, i.e., [log.sub.2 N] stages for N-bit operands.
FIG. 9 represents a typical nodal processor 10 located at, say, node l, k of FIG. 8 producing G.sub.l,k at its output. Processor 10 accepts as input operands G.sub.l-1, k-2.sup.l-1, G.sub.l-1,k and P.sub.k P.sub.k-1 . . . P.sub.k-2.spsb.l-1 at its input terminals 11, 12 and 13 respectively. "AND"-gate 16 and "OR"-gate operate on these inputs to produce at output 14 the boolean function
FIG. 10 is an embodiment of an 8-bit carry generator having four rows (0-3) and 8 columns (0-7). Rows 1 through 3 comprises 7, 6 and 4 nodal processors 10, respectively, each of the type depicted in FIG. 9. Row 0 comprises 8 AND-gates 20 arranged to accept at input terminals 301 corresponding operand bit pairs, {A.sub.k, B.sub.k }, forming G.sub.0,k =A.sub.k *B.sub.k and supplied to processors 10 on line 11. The processors 10 of row 1 also accept the seven propagation variable P.sub.1, through P.sub.7 on input lines 305. Propagation variable P.sub.k being applied as an input to processor 10 located at row 1, column k on line 13 together with G.sub.0,k-1 supplied by lines 12. The output of processor 10 located at 1,k is
In a similar manner, processors 10 of row 2 are supplied the outputs of row 1 together with propagation variable P.sub.21 through P.sub.76 from input line 307. The output of processor 10 located at 2, k is
from inputs provided by lower level processors and propagation variable P.sub.4 P.sub.3 P.sub.2 P.sub.1 through P.sub.7 P.sub.6 P.sub.5 P.sub.4 supplied on input lines 309.
Carry output C.sub.0 is available directly from AND-gate 20 at location 0,0 on line 303; C.sub.1 from output line 14 of processor 10 at location 1,1; C.sub.2 and C.sub.3 from processors 10 at location 2,2, and 2,3 respectively; and C.sub.4 through C.sub.7 from row 3 processor 10 outputs.
FIG. 11 is a logic circuit for implementing an 8-bit propagation generator suitable for supplying propagation variables to the 8-bit carry generator of FIG. 10. Propagation generator 400 comprises 7 OR-gates 40 in row 0 used to form propagation variables P.sub.1, P.sub.2, . . . P.sub.7 from input operand bit pairs {A.sub.k, B.sub.k } as follows:
The set, {P.sub.k }, is available on output lines 305. Subsequent rows are comprised of AND-gates 50. The k.sup.th AND-gate of row 1 accepts the k.sup.th and k-1.sup.th output of row 0 to form, at its output 307, P.sub.k P.sub.k-1. Similarly, the kth processor of row 2 accepts the k.sup.th and k-2.sup.th output of row 1 to form the set of propagation variables, {P.sub.k P.sub.k-1 P.sub.k-2 P.sub.k-3 }, provided at output 309.
FIG. 12 represents a logic network 60 for forming the complete bit sum of two operand bits (A.sub.k, B.sub.k) and a carry-in bit, Ck, comprising exclusive-or (EOR) networks 61 and 62. EOR network 61 forms the modulo-2 sum A.sub.k ⊕B.sub.k and network 62 produces at its output
S.sub.k =A.sub.k ⊕B.sub.k ⊕C.sub.k-1
Note that carry C.sub.N-1 is available at the output as an overflow bit of for use in extending the number of bits in the operands A and B.
FIG. 14 is a block diagram of an m-bit wide, 2-level module 500 comprising two layers of m nodal processors 10 of the type shown in FIG. 9. Five sets of m-input lines are accommodated: inputs 501 accept the corresponding I-level outputs, {G.sub.l,k }; inputs 503 accept the I-level outputs displaced by 2.sup.I-1, {G.sub.l,k-2.sup.I-1 }; inputs 505 and 507 accept the propagation carry-terms ##EQU5## respectively; and inputs 509 accept the (I+1).sup.th inner layer output terms (displaced by 2.sup.I), {G.sub.I+1,k-2.sup.I }.
Two sets of output lines are provided: outputs 511 correspond to the first layer output terms, {G.sub.I+1,k }; and outputs 513 are the second layer (or module) outputs, {G.sub.I+2,k }.
FIG. 15 is an interconnection diagram for a carry generator 300 using 4-bit wide (m=4) 2-layer modules 500. Each logic unit 520 represents a set of four unit 20 AND-gates used to form {G.sub.k }.
FIG. 15 may be best understood by referring to FIG. 16 that shows the matrix equation relating the zero level (I=0) inputs, {G.sub.0,k }, to the second level (I=2) outputs, {G.sub.2,k }, and to FIG. 17 showing the matrix equation relating the second level outputs to the fourth level outputs, {G.sub.4,k }. In FIG. 16, the two 16 (P.sub.1.sup.(16), P.sub.2.sup.(16)) are each partitioned into 16 4 single layer 4-bit wide operation performed within a 500 module. The submatrices of the right-hand matrix correspond to first layer operations while those in the left-hand matrix correspond to the second layer operations previously described. Similarly, the right hand set of submatrices in FIG. 17 corresponds to third level (I=3) operations and the left set corresponds to fourth level (I=4) operations. These equations provide interconnect information by relating the individual module 500 inputs to their outputs.
This latter equation expresses the required inputs to module 500 (1,3): the first expression on the right implies only two non-zero products ##EQU7## thus requiring ##EQU8## as inputs; the second expression requires ##EQU9## and the third requires the input quadruplet [G.sub.0,8 G.sub.0,9 G.sub.0,10 G.sub.0,11 ].sup.T, and the triplet ##EQU10## Summarizing, the required inputs are: G.sub.0,8-11, G.sub.1,6-7, G.sub.0,7, and ##EQU11## as shown in FIG. 15. (Please note that for FIG. 15, the output carries, {C.sub.k }, are equal to {G.sub.4,k }.)
Another preferred embodiment using a slightly different concept of modularity is shown in FIG. 19. For purposes of explanation, a 24-bit adder network is shown comprising: three 8-bit conditional adder networks 141 each accepting two eight bit operands [(A.sub.0-7, B.sub.0-7), (A.sub.8-15, B.sub.8-15), (A.sub.16-23, B.sub.16-23)], and each outputting two conditional 8-bit sums (S.sub.E, S.sub.N) as previously described in FIG. 1; multiplexer units 160 for selecting the S.sub.E or S.sub.N output of each conditional adder unit which is controlled by a two state carry signal; carry and propagation generator units 600 each comprising a carry generator 300' and propagation generator 400' for accepting two 8-bit operands and producing at its output the highest carry, say C.sub.7, out of a possible set of (C.sub.0, C.sub.1, . . . , C.sub.7) for controlling its associated 2:1 MUX 160. Note that the lowest order (extreme right) MUX 160 is shown dotted so as to indicate that modularity consideration may require that each 8-bit conditional adder 141 be packaged with an associated MUX 160, in which case its control but would be set low because the absence of an input carry makes the S.sub.N output always valid. In effect, each of the three vertical grouping of units 141, 160 and 600 constitute a modular adder and carry-out generator 700 requiring its associated two fields of operand bits and carry-in bit. The tandem ensemble of these units makes-up the complete adder. The output sum is represented by the 25-bit sum S.sub.0-7, S.sub.8-15, S.sub.16-23, S.sub.24.
In order to accommodate the carry-in bits (C-1, C7, C15) to units 600, a slight modification of the basic matrix and flow diagram must be made. Consider, the unit 600 shown on the extreme right of FIG. 19. The requisite matrix has the form ##STR2## Note that if the carry-in, C.sub.-1, is zero (non-existent), the first row and column are effectively zero. Also, P.sub.0 =C.sub.-1 so that P.sub.0 and all its product terms vanish if C.sub.-1 =0. Thus, when C.sub.-1 =0, networks 300 and 400 are as previously defined. If C.sub.1 =1, then the form of the matrix, carry-generator network 300 and propagation generator 400 have the same logic structure as previously described.
For example, FIG. 20 shows the flow diagram corresponding to a 4-bit carry-generator 300 with an input carry bit C.sub.-1, suitable for concatenating 4-bit conditional adder units in a similar fashion to that shown for 8-bit conditional adder units 141 in FIG. 19. The necessary steps required for generating the output carry, C.sub.3, are shown by solid lines while the dotted-lines represent the other possible, but not required, processing steps previously shown. This implies the carry-out generator structure 300' shown in FIG. 21 using processing modules 10.
FIG. 24 shows a simplified block diagram for propagation generator 400' suitable for use with the 8-bit adder module 700 of FIG. 19. The subset of propagation terms required the 4-bit carry-out generator 300' (P.sub.3 P.sub.2 P.sub.1 P.sub.0, P.sub.3 P.sub.2, P.sub.3, P.sub.1) is also available from this unit.
The same flow diagram and logic networks are applicable to all concatenated units 600 of FIG. 19. However, in the case of the lowest significant unit 600 at the extreme right of FIG. 19, the carry-in from the previous stage is non-existent so that C.sub.-1 =0. For the other stages, the carry-out of the previous section is used as the carry-in.

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