Floating-point conversion and arithmetic

Adding floating-point numbers

1. Normalise
2. Match the exponent
3. Add the mantissas

Using 8.4 two's-complement floating-point, add 01011101​0111 and 01111000​0101

A = 01011101​0111
B = 01111000​0101 = 00011110​0111
A + B = (01011101 + 00011110)0111 = 01111011​0111

Exercises

1. Using 8.4 two's-complement floating-point, add 01100101​0101 and 01011010​0011

   A = 01100101​0101
   B = 01011010​0011 = 00010110​0101
   A + B = (01100101 + 00010110)0101 = 01111011​0101

2. Represent the number 55 in normalised two's-complement floating-point notation, using as few bits as possible

   55 = 0110111 = 0.110111 « 6 = 0110111​0110 (7.4)

3. A computer represents numbers using normalised 6.4 two's-complement floating-point representation (why though, it's 10 bits).

   Add the following three numbers together and give the answer in the format described. You must show your working.

   010100  0010
   011000  0001
   100010  0010
   ------------ shift mantissas so exponent == 0010
   010100  0010
   001100  0010
   100010  0010
   ============ add mantissas
   000010  0010
   ------------ normalise
   010000  1111