Question

Write down the binary representation of the decimal number 126.5 assuming the IEEE 754 single precision format. (Show your steps)

Answer 1

126.5
126.5 in simple binary => 1111110.1
so, 126.5 in normal binary is 1111110.1 => 1.1111101 * 2^6

single precision:
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sign bit is 0(+ve)
exp bits are (127+6=133) => 10000101
frac bits are 11111010000000000000000

so, 126.5 in single-precision format is 0 10000101 11111010000000000000000
in hexadecimal it is 0x42FD0000