Question

1.Represent the following decimal numbers using IEEE-754 floating point representation:

a.-25

b.-9.25

Answer 1

a)
-25 in simple binary => 11001
so, -25 in normal binary is 11001 => 1.1001 * 2^4

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+4=131) => 10000011
frac bits are 10010000000000000000000

so, -25 in single-precision format is 1 10000011 10010000000000000000000
in hexadecimal it is 0xC1C80000

b)
-9.25 in simple binary => 1001.01
so, -9.25 in normal binary is 1001.01 => 1.00101 * 2^3

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+3=130) => 10000010
frac bits are 00101000000000000000000

so, -9.25 in single-precision format is 1 10000010 00101000000000000000000
in hexadecimal it is 0xC1140000