I'm trying to understand binary floating point and using just a 4-bit mantissa and a 4-bit exponent (both 2s compliment) to keep things simple.

As far as I can tell, the largest denary number I can represent is 112: 0111 0111

So why do I have trouble representing denary 11 (eleven) in this system? I get that the largest (positive) mantissa is 7 in denary (0111). So I'm inferring that I can't represent consecutive positive integers between 0 and the maximum value of 112.

Is that correct? If so, can someone help me to see why please? Which numbers in this range can I represent?


Yes, that is correct. Your mantissa has only three magnitude bits, so you can only represent numbers from -8 to 7, multiplied of course by any power of 2 from $2^{-8}$ to $2^7$. 11 is impossible to represent, because any positive exponent gets you multiples of 2, any negative exponent gets you numbers less or equal to $7*2^{-1}=3.5$, and exponent 0 is just numbers from -8 to 7.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.