Question

For IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values:

0.6

Answer 1

0 =0

0.6 =0.1001 1001 1001 1001 1001 1001

Normalize the binary representation

1.0011 0011 0011 0011 0011 001 × 2-1

Sign: 0 (a positive number)

Exponent (unadjusted): -1

Mantissa (not normalized): 1.0011 0011 0011 0011 0011 001

Exponent (adjusted) =Exponent (unadjusted) + 2(8-1) - 1 =-1 + 2(8-1) - 1 =(-1 + 127)(10) =126 = 0111 1110

Sign (1 bit) =

0 (a positive number)

Exponent (8 bits) =

0111 1110

Mantissa (23 bits) =

001 1001 1001 1001 1001 1001

0 - 0111 1110 - 001 1001 1001 1001 1001 1001

in hexadecimal

0 7E 199999