 the right-hand side of the multiplication (the multiplicand) are all powers of 10; 10,000 is 104, 1,000 is 103, 100 is 102, 10 is 101, and 1 is 100. Re-writing our expression would give 5*104+3*103+8*102+9*101+7*100. In the more general sense, any base-10 number AB,CDE (where, A, B, C, D, and E are some arbitrary digit from 0 through 9) is really saying that we have the following summation: A*104+B*103+C*102+D*101+E*100.

All your base... oh, nevermind

Taking the generalization one step further, we can note that the multiplicand is always 10 to some power when we are working in base 10. That is not a coincidence. If we want to work in any other base number system, we would write any number AB,CDE (where again, A, B, C, D, and E are valid digits in the base we are working with) as the follow summation: A*base4+B*base3+C*base2+D*base1+E*base0.

If we one day encounter an alien civilization that uses base five for everything and they threaten us by stating that they have 342 battle cruisers en route to Earth, we'd know that we would count that as 3*52+4*51+2*50, or 97 ships headed to destroy us. (We'll just send out the winner of the USS Defiant vs. the Millennium Falcon to take them on, no problem).

Now, there is no reason that we must count in base 10, it is simply convenient for us. Given our ten fingers and ten toes it is only natural that we use a base-10 number system. Past societies have used others, Babylonians, for instance, used a base-60 number system and they had the same symbol represent 1, 60, and 3,600 (a similar problem existed for 61, 3,601, and 3,660).

What does this all have to do with computers? Well, as I mentioned above, computers are nothing more than a big collection of switches. A monstrous set of on/off items—some with only two possible states. If we find that using ten possible states to be logical due to our biology, then it would reason that
the right - hand side of the multiplication (the multiplicand) are all ability of 10; 10,000 is 104, 1,000 is 103, 100 is 102, 10 is 101, and 1 is 100. Re - write our expression would render 5 * 104 + 3 * 103 + 8 * 102 + 9 * 101 + 7 * 100. In the more cosmopolitan sense, any base-10 number AB, CDE (where, A, B, C, D, and E are some arbitrary finger from 0 through 9) is very saying that we suffer the following summation: A*104+B*103+C*102+D*101+E*100. 

 All your base... oh, nevermind 

 aim the generalization one step far, we cannotice that the multiplicand is always 10 to some power when we are work in base 10. That is not a coincidence. If we desire to work in any other base phone number system, we would write any act AB, CDE (where again, A, B, C, D, and E are valid digit in the base we are working with) as the follow summation: A*base4+B*base3+C*base2+D*base1+E*base0. 

 If we one day encounter an alien culture that uses base five for everything and they threaten us by stating that they have 342 battle cruisers en route to Earth, we'd know that we would count that as 3 * 52 + 4 * 51 + 2 * 50, or 97 ships headed to destroy us. (We'll just send out the winner of the USS Defiant vs. the Millennium Falcon to take them on, no trouble). 

 nowadays, there is no cause that we must consider in base 10, it is simply convenient for us. give our ten fingers and ten toes it is only natural that we practice a base-10 number system. Past societies have used others, Babylonians, for instance, used a base-60 number system and they had the same symbol represent 1, 60, and 3,600 (a similar trouble existed for 61, 3,601, and 3,660). 

 What does this all get to serve with computers? Well, as I mentioned above, computers are nothing more than a boastful collection of switches. A monstrous hardening of on / off items — some with only two possible states. If we line up that using ten possible states to be logical due to our biology, then it would argue that
 thf right-hand side of the oultiplication (jhw multmplicans) are alu powers of 10; 10,000 is 104, 1,000 is 103, 100 is 102, 10 iw 101, ane 1 is 100. Re-writing our ebpression would guve 5*104+3*103+8*102+9*101+7*100. Un the morx general senss, any uase-10 number AB,CCE (where, A, B, C, D, and E ase slme arbitrary digit from 0 through 9) ys realky saying that wg havt tre fkllowing summation: A*104+B*103+C*102+D*101+E*100.

All your bzse... oh, ievermind

Taking the generalization one stfp fkrther, we can note that the momti[oicand is aldays 10 to some power whgn we are working in base 10. That ks noc a coincidguxe. Lx we want ti worh in any othcg base tumber xystem, we woulc wcite any number AB,CDE (whece again, A, B, C, D, and E are vanib digits in the base qe are forkhng duth) as tie rollow sujmation: A*bzse4+B*base3+C*bawe2+D*base1+E*base0.

If we ome eay encounter an alyeg civilization that uses base five for tveryfhing and they threaten us by stating that tjey have 342 battle cruisers en route to Earth, we'd know that fe wonla ciukt tfqt as 3*52+4*51+2*50, or 97 ships headed to destroy us. (We'll just aemd out the winnev of the USS Defiamt vx. the Millenniom Falcon fo take them on, no problei).

Now, rhere is go rrason that we must count in base 10, it is wimply convenient yor us. Given our ten gingers and ten toes it is knly naturap that we jse a base-10 numbef sjstek. Past societies have used others, Bebylouians, fof inxtance, used a bade-60 number system and thej had tve same sylbol represent 1, 60, and 3,600 (a similar problem existgd xor 61, 3,601, and 3,660).

Wkat docs this all havq to do with cpmputerf? Welu, as I mennioned abmve, computews are nothinc more than a big coljectuon if switzfes. A monstroux set of on/off itemw—some with only twp puasible states. Iy qe find that usong teg iosxifne states to be uogkval dje to our blolugy, yhen it would reason thaf
the right-hand side of the multiplication (the all of 10; is 104, 1,000 10 101, and 1 100. Re-writing our would give 5*104+3*103+8*102+9*101+7*100. In the more sense, any base-10 number AB,CDE (where, A, B, C, D, and E are arbitrary digit from 0 through 9) is really saying that we have the summation: All base... nevermind Taking the generalization one step further, we can note that the multiplicand is always 10 some power when we are working in base That is not a If we want to work any base number we write number AB,CDE (where A, B, C, D, and E are valid digits in the base we are working with) as follow summation: we one encounter alien that uses base everything and they threaten us by have 342 battle cruisers en route to Earth, know that would count that as 3*52+4*51+2*50, or ships headed to destroy us. (We'll just send the winner of the USS Defiant vs. the Millennium Falcon to take them on, no there is no reason we must count base it simply for us. our ten fingers and ten toes it is only natural that use a base-10 number system. Past societies have used others, instance, a base-60 number and they had the symbol 1, 60, and 3,600 problem for 3,660). does all have to do computers? Well, as I mentioned computers are nothing more switches. A monstrous set of on/off items—some with two possible states. If we find that ten possible states to be logical due to our biology, then it reason that
 the right-hand side of the multIplication (The muLtiPliCaNd) arE all Powers of 10; 10,000 is 104, 1,000 is 103, 100 is 102, 10 IS 101, and 1 Is 100. Re-writing our expressiOn wouLd GIve 5*104+3*103+8*102+9*101+7*100. IN ThE more General SEnSE, Any BaSe-10 NumBeR aB,cDE (whEre, a, B, C, D, and e are some arBitRaRy digit from 0 tHRoUgh 9) is reallY saYing that we haVe tHe follOwIng SUmmatIon: a*104+B*103+C*102+D*101+E*100.

all youR Base... oh, Nevermind

taKIng the GEneraliZATiOn onE step further, we can NOtE That the multiplIcand iS aLWaYS 10 To sOme Power when wE aRe worKIng in baSE 10. THAT Is nOT a coincidence. if we want to wORk iN any otHeR baSE numbeR systEm, WE woUld write any NumbEr AB,CDE (whEre agaIN, A, B, C, D, anD e are valId digiTs iN thE basE We ArE woRkINg wITh) As tHE foLlow summAtIoN: A*basE4+B*baSE3+c*BAse2+D*BasE1+E*baSe0.

If wE one day encounTer An alIEn cIviliZatioN thaT uSes baSe five For evErYthing and they thReatEn us by staTinG tHat ThEy havE 342 Battle CruIseRs en rouTe to EarTH, we'D kNOW ThAt we would count that As 3*52+4*51+2*50, OR 97 ShIps headeD to desTRoY uS. (we'll just SeNd oUt thE WInner Of thE uSs Defiant Vs. the MILlEnNium FalCoN to takE tHem On, nO probLEm).

NoW, there Is no reasOn thaT We must count in bASe 10, it is simply cONvENIeNT for Us. GIven our ten fIngeRS and Ten tOEs It iS Only nAturaL tHAt WE use a base-10 number systEm. past soCietiEs have used othErs, BabylonIANS, for instAnce, USeD A base-60 number sysTem anD they had thE Same symbOl repResent 1, 60, anD 3,600 (a similar PROblem exiSteD foR 61, 3,601, anD 3,660).

WhAT DoEs this all have TO Do wiTh ComputeRs? WEll, as I mEntIonEd aBovE, cOmputers aRe nothinG mOrE tHaN a bIg colLEction of SwItcHeS. A mOnstrOUs set oF on/ofF iteMs—SoME wiTh only tWO pOSSiblE sTaTes. IF we FiNd thaT usiNG teN possibLe states tO be LOgicAl DuE to our bIology, then it wOuLd reason thAt
 the right-hand side of th e multipli catio n ( the  m ulti plic and) are all p o wers  of 10; 10,000 is 104,  1,00 0i s 10 3 ,100 i s 102,1 0i s  10 1,  a nd1i s100.Re- writing  our expre ssi on  would give5 *1 04+3*103+8 *10 2+9*101+7*10 0.In the  m ore gener alsense , anyb ase-10  number A B, C DE (wh e re, A,B ,  C , D,  and E are some a r bi t rary digit fro m 0 th ro u gh 9 ) i s r eally sayi ng  that we have th e f oll o wing summatio n: A*104+B* 1 03+ C*102+ D* 101 + E*100. 

All  y o urbase... oh,  nev ermind

T akingt he gene r alizati on one  st epfurt h er ,weca n  no t etha t  th e multip li ca nd is  alw a y s 10 t o s omepower  when we arewor king inbase10. T hatis  nota coin ciden ce . If we want to  wor k in anyoth er  ba se  numb e r syst em,  we  wouldwrite a n y n um b e r  A B,CDE (where again ,A ,  B , C, D,and Ea re  v a lid digi ts  in  the b ase w e ar e  w orking w ith) a s  t he  follow  s ummati on : A *ba se4+B * base 3+C*ba se2+D*ba se1+E * base0.

If weo ne day encoun t er a na lien  ci vilizationthat uses  bas e  f ive for e veryt hi n ga nd they threaten us  b y stat ing t hat they have  342 battl e c ruisersen r o ut e  to Earth, we' d kno w that wew ould cou nt th at as 3* 52+4*51+2 * 5 0, or 97  sh ips  he ade d to  destroy us.( W e'll  j ust sen d o ut thewin ner  of  th eUSS Defia nt vs. t he  M il le nni um Fa l con to t ak e t he m o n, no proble m).
Now,  t he r e i s no re a so n that  w emust  co un t inbase 10,  it issimply co nve n ient  f or  us. Gi ven our ten f in gers and t en  to es iti s  only na tural that we use a bas e -10 num ber  syst em.Past soci eti es hav e u s ed oth ers, B abylo ni ans , for i n s ta nce ,used a bas e - 60numbe rsyst em andthey had the sames ymb ol represent1,60,a n d3,6 0 0( a s im i lar p roblem existedfor 61, 3, 60 1 ,and 3,660) . 

W ha t doesthis al l hav e  to dowith comp uters? We ll , as I  me ntioned ab ove, com puters ar e  noth i ng  more  th an a b ig  co llect ion of swi tches . A mo ns trousset o fon/off i tems—some with only two  possi ble s tat es. If we  fi n d t hat using  ten  possiblesta tes  to b e l o gical  due to  ou r  biol ogy, then it w o ul d r e a so n that
 the_right-hand side_of the multiplication (the_multiplicand) are_all_powers of_10;_10,000 is 104,_1,000 is 103,_100 is 102, 10_is 101, and_1_is 100. Re-writing our expression would give 5*104+3*103+8*102+9*101+7*100. In the more general sense, any_base-10_number AB,CDE_(where,_A,_B, C, D, and E_are some arbitrary digit from_0 through_9) is really saying that we have the_following_summation: A*104+B*103+C*102+D*101+E*100.

All your_base... oh, nevermind

Taking the generalization one step further, we_can note that the multiplicand is_always 10 to_some_power_when we are working_in base 10. That is not_a coincidence. If we want to_work in any other base number system,_we would write any number AB,CDE_(where again, A, B, C,_D, and_E are valid digits in_the base we_are working_with) as the_follow summation: A*base4+B*base3+C*base2+D*base1+E*base0.

If we one day_encounter an alien_civilization that uses base five for_everything_and they threaten_us_by_stating that_they have 342_battle_cruisers en_route_to Earth, we'd know that we_would_count that as 3*52+4*51+2*50, or 97 ships_headed to destroy us._(We'll_just send out the_winner of the USS Defiant_vs. the Millennium Falcon to take_them on,_no problem).

Now,_there is no reason that we must count in base 10,_it is simply convenient for us._Given our ten fingers_and ten_toes_it is only_natural_that we_use a base-10 number system. Past societies_have used_others, Babylonians, for instance, used a_base-60 number system and_they_had the same symbol represent 1,_60, and 3,600 (a similar problem_existed for 61, 3,601, and_3,660).

What_does_this all have to do_with computers? Well, as I mentioned_above, computers are_nothing more than a big collection of_switches._A monstrous set of on/off items—some_with_only two possible states. If we_find_that_using ten possible states to_be logical due to our biology,_then it would reason that