For example, binary representation of 65535 is 1111111111111111 in 16 bit representation. The number 65535 depends on the value at each bit, but can we comment on relationship among the bits if we are given a number and it is represented in binary form.
If you mean some kind of correspondence between decimal digits and bits in binary representation of the same number, then probably no such obvious correspondence may be given. This is in contrast to octal or hexadecimal notation: here every octal (or hexadecimal) digit has always the same binary representation, for example:
6 (octal) = 110 (binary) = 0110 (hex) = 6 (decimal)
7 (octal) = 111 (binary)
C (hex) = 13 (decimal) = 1010 (binary)
More specifically, a single octal digit always is represented as 3-bit sequence, and a single octal digit - as a 4-bit sequence, where leading zeroes (zero bits), if any, may be omitted *only* at the begining of the said number.
This is fine for integer numbers. When fractions are allowed, things get more complicated as their binary (or decimal) representations need not to be unique (nor even finite ..), see: 1.0 = 0.9999.... (decimal). But that's another story, especially when you deal with finite-length binary arithmetic, as computers do. Here, even very simple cases, as 0.1 (decimal, finite length representation) often translate into infinite binary fraction.
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Publication