Question

Represent -1.25e2 in IEEE-754 32-bit floating-point form, where the exponent is 8bit and the bias is 127. Give the answer as a 32-bit binary number, without any space between the bits.

Answer 1

Sign 1 Bit

Exponent(8 bits)

Mantissa(23 bits)

IEEE-754 32-bit floating-point form

Given -1.25e2 to be represented in IEEE-754 32-bit floating-point form

-1.25e2 = -125

Now we convert -125 to binary, here I am using successive division method

(-125)10 = (-1111101)2

(-1111101)2 = - 1.111101 X 26

Since the number is negative sign bit must be set to 1

Mantissa = 111101000000000000000000

Exponent is actually biased so we add 127 to get the value so exponent 127+6 = (133)10

Again using successive division method

So exponent is 10000101

So the answer is

Sign         Exponent                                Mantissa

1

10000101

111101000000000000000000