Question

please explain comment out your steps

Find the IEEE-754 single binary representation in hexadecimal of 78.75_10.

a. 429D8000 b. 42498000 c. 42589000 d. 42489000

Answer 1

78.75 in simple binary => 1001110.11
so, 78.75 in normal binary is 1001110.11 => 1.00111011 * 2^6

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+6=133) => 10000101
frac bits are 00111011000000000000000

so, 78.75 in single-precision format is 0 10000101 00111011000000000000000
in hexadecimal it is 0x429D8000

Answer: a.  429D8000