title: c - understanding floating point binary model
body: <p>So I'm having trouble understanding floating point binary representation. I have an image below from my teacher's notes but I don't understand how they got the string of digits for the 8-bit exponent and 23-bit mantissa for each of the rows. </p>
  
  <p>So the teacher represents 284 as 100011100 = 1.000111 x 2^8. I get that the bit sign is 0 because it's a positive number. I have no idea where the 8-bit exponent of 00001000 came from, and the 23-bit mantissa seems to be a larger representation of 1.000111 that fills in 23 bits.</p>
  
  <p>I was wondering if someone could explain how the teacher was able to fill in the chart/get the values from converting 100011100 into 1.000111 x 2^8? I tried watching tutorials and looking on other sites but I'm still very confused.</p>
  
  <p>I would also appreciate if someone could explain how the teacher went from having the values in the first row to changing them to an 8-bit exponent of 10000111 and a 23-bit mantissa of 000 1110 0000 0000 0000 0000 as shown in the 3rd row. Any help would be appreciated, I've been staring at this part of my notes for hours but I just can't seem to comprehend the logic behind all this. It all seems so complex and overwhelming.</p>
  
  <p><a href="https://i.stack.imgur.com/ayqjm.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ayqjm.png" alt="enter image description here"></a></p>