Question

6. Now that you've worked up an appetite for number conversions, represent -2.625 as an IEEE single precision floating point number. Give your answer in both binary and hex adecimal and show your work. Is the representation exact?

Answer 1

-2.625


2.625 in normal binary is 2+0+0.5+0.125 => 10.101 => 1.0101 * 2^1
so, 2.625 in binary is 1.0101 * 2^1

sign bit is 1(-ve)
exp bits are (127+1=128) => in binary it is 10000000
frac bits are 01010000000000000000000

-2.625 in IEEE single precision format is 1 10000000 01010000000000000000000

In hexadecimal it is 0xC0280000
IN binary it is 11000000001010000000000000000000