here is an example of floating point representation ... I am unable to understand whats going on. book isnt much help except that I know the bias part and that the matissa is 23 bit and exponent is 8 bits. however I don't understand how the conversion is being done how the 0 and 1 are being generated. can some wise man/woman out there help me understand this... thanks
Convert 0.1015625 to IEEE 32-bit floating point format.
Converting:
0.1015625 × 2 = 0.203125 0 Generate 0 and continue.
0.203125 × 2 = 0.40625 0 Generate 0 and continue.
0.40625 × 2 = 0.8125 0 Generate 0 and continue.
0.8125 × 2 = 1.625 1 Generate 1 and continue with the rest.
0.625 × 2 = 1.25 1 Generate 1 and continue with the rest.
0.25 × 2 = 0.5 0 Generate 0 and continue.
0.5 × 2 = 1.0 1 Generate 1 and nothing remains.
So 0.101562510 = 0.00011012.
Normalize: 0.00011012 = 1.1012 × 2-4.
Mantissa is 10100000000000000000000, exponent is -4 + 127 = 123 = 011110112, sign bit is 0.
So 0.1015625 is 00111101110100000000000000000000 = 3dd0000016