Question

Determine the single precision and double precision machine representation of -200.0625

Single__________________(16)

Double__________________(16)

Would you please show me the steps.

Thank you!

Answer 1

-200.0625 in simple binary => 11001000.0001
so, -200.0625 in normal binary is 11001000.0001 => 1.10010000001 * 2^7

single precision:
--------------------
sign bit is 1(-ve)
exp bits are (127+7=134) => 10000110
frac bits are 10010000001000000000000

so, -200.0625 in single-precision format is 1 10000110 10010000001000000000000
in hexadecimal it is 0xC3481000

double precision:
--------------------
sign bit is 1(-ve)
exp bits are (1023+7=1030) => 10000000110
frac bits are 1001000000100000000000000000000000000000000000000000

so, -200.0625 in double-precision format is 1 10000000110 1001000000100000000000000000000000000000000000000000
in hexadecimal it is 0xC069020000000000

single: 0xC3481000
double: 0xC069020000000000