How many bytes with this configuration given in bits?

Question

If the maximum number of bits of certain field is set to be 10 bits max. How many bytes can be set within this limitation?

The solution of such a problem suggests number of bytes ranged is 1023. Can anyone help me find why?

Thanks

Answer 1

Ten bits of binary give you $2^{10}=1024$ options. If you start counting at $0$, you can count up to $1023$.

Answer 2

If you need to get away with using just one index, then you can represent $2^{10}=1024$ distinct values. But if you are allowed to use two values you could have one point at some vector of index offsets. This is what is needed to be done in 32 bit OS:es when disks and/or internal memory larger than $2^{32} = 4 gigs$ of memory, and also the famous "640 kB should be enough for everyone" most computers and operating systems at the time had to suffice with 64kB or 16 bits of adress space so 10 whokle pages should have sounded like a lot. Which it probably did for the first year or two.