Question

Convert the following binary floating point  to decimal

IEEE 32-bit floating point format.  

0 1000 0101 000 0100 1101 0000 0000 0000

Answer 1

0 10000101 00001001101000000000000
sign bit is 0(+ve)
exp bits are 10000101
   => 10000101
   => 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+0x2^1+1x2^0
   => 1x128+0x64+0x32+0x16+0x8+1x4+0x2+1x1
   => 128+0+0+0+0+4+0+1
   => 133
in decimal it is 133
so, exponent/bias is 133-127 = 6
frac bits are 00001001101

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.00001001101 * 2^6
1.00001001101 in decimal is 1.03759765625
   => 1.00001001101
   => 1x2^0+0x2^-1+0x2^-2+0x2^-3+0x2^-4+1x2^-5+0x2^-6+0x2^-7+1x2^-8+1x2^-9+0x2^-10+1x2^-11
   => 1x1+0x0.5+0x0.25+0x0.125+0x0.0625+1x0.03125+0x0.015625+0x0.0078125+1x0.00390625+1x0.001953125+0x0.0009765625+1x0.00048828125
   => 1+0.0+0.0+0.0+0.0+0.03125+0.0+0.0+0.00390625+0.001953125+0.0+0.00048828125
   => 1.03759765625
so, 1.03759765625 * 2^6 in decimal is 66.40625
so, 01000010100001001101000000000000 in IEEE-754 single precision format is 66.40625
Answer: 66.40625