Binary multiplier In binary encoding each long number is multiplied by one digit (either 0 or 1), and that is much easier than in decimal, as the product by 0 or 1 is just 0 or the same number. Therefore, the multiplication of two binary numbers comes down to calculating partial products (which are 0 or the first number), shifting them left, and then adding them together (a binary addition, of course): This is much simpler than in the decimal system, as there is no table of multiplication to remember: just shifts and adds. This method is mathematically correct and has the
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