Question

Convert the following floating-point number (stored using IEEE floating-point standard 754) to a binary number in non-standard form.

0100_0001_1110_0010_1000_0000_0000_0000

Answer 1

0 10000011 11000101000000000000000
sign bit is 0(+ve)
exp bits are 10000011
Converting 10000011 to decimal
   10000011
   => 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+1x2^1+1x2^0
   => 1x128+0x64+0x32+0x16+0x8+0x4+1x2+1x1
   => 128+0+0+0+0+0+2+1
   => 131
in decimal it is 131
so, exponent/bias is 131-127 = 4
frac bits are 11000101

IEEE-754 binary value is 1.frac * 2^exponent
IEEE-754 binary value is 1.11000101 * 2^4 = 11100.0101
Answer: 11100.0101

1.11000101 in decimal is 1.76953125
   => 1.11000101
   => 1x2^0+1x2^-1+1x2^-2+0x2^-3+0x2^-4+0x2^-5+1x2^-6+0x2^-7+1x2^-8
   => 1x1+1x0.5+1x0.25+0x0.125+0x0.0625+0x0.03125+1x0.015625+0x0.0078125+1x0.00390625
   => 1+0.5+0.25+0.0+0.0+0.0+0.015625+0.0+0.00390625
   => 1.76953125
so, 1.76953125 * 2^4 in decimal is 28.3125
so, 01000001111000101000000000000000 in IEEE-754 single precision format is 28.3125

Answer in binary:   11100.0101
Answer in decimal:  28.3125