16.75 How to convert to floating point representation?

Question

16.75 convert to base 2 floating point representation.

Need help on formula, Thanks.

Answer 1

$16=2^4$ and $0.75=3/4=3\times 2^{-2}$. Therefore $16.75_{10}=10000.11_2.\;$ Or do you want to have IEEE floating point format (for single, double)?

The IEEE double is computed as: sign bit $= 0,\;$ exponent $4+1023,\;$ significand including high bit =$100001100000000\dots$. Omitting the leading significand bit and combining the parts give

0 10000000011 0000110000000000000000000000000000000000000000000000

written in 4-bit blocks

0100 0000 0011 0000 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

or as hexadecimal

4030C00000000000

Answer 2

Note $16.75=2^4+2^{-1}+2^{-2}$ so in base $2$ we have $10000.11=1000011\cdot2^{-2}$