Binary number digit represents. For example, the binary number 100101 is converted to decimal form as follows: Fractions in binary only terminate if the denominator has 2 as the only prime factor. As a result, 1/10 does not have a finite binary representation, and this causes 10 × 0.1 not to be precisely equal to 1 in floating point arithmetic. As an example, to interpret the binary expression for 1/3 = .010101..., this means: 1/3 = 0 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + ... = 0.3125 + ... An exact value cannot be
Signed number representations as the largest positive number that can be represented, and vice versa if the word has an odd number of bits. The following table shows the positive and negative integers that can be represented using four bits. Same table, as viewed from "given these binary bits, what is the number as interpreted by the representation system": Google's Protocol Buffers "zig-zag encoding" is a system similar to sign-and-magnitude, but uses the least significant bit to represent the sign and has a single representation of zero. This allows a variable-length quantity encoding intended for nonnegative (unsigned) integers to be used efficiently for