Question

Using IEEE 754 representation for single precision floating point, give the 32-bit binary encoding for the numbers below.

Show the sign, exponent, and mantissa (significand).

a. -2.40625

b. 11.2265625

Answer 1

a)
-2.40625 in simple binary => 10.01101
so, -2.40625 in normal binary is 10.01101 => 1.001101 * 2^1

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+1=128) => 10000000
frac bits are 00110100000000000000000

so, -2.40625 in single-precision format is 1 10000000 00110100000000000000000
sign => 1
exponent => 10000000
mantissa => 00110100000000000000000

b)
11.2265625 in simple binary => 1011.0011101
so, 11.2265625 in normal binary is 1011.0011101 => 1.0110011101 * 2^3

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+3=130) => 10000010
frac bits are 01100111010000000000000

so, 11.2265625 in single-precision format is 0 10000010 01100111010000000000000
in hexadecimal it is 0x4133A000
sign => 0
exponent => 10000010
mantissa => 01100111010000000000000