Binary Arithmetic

Binary Arithmetic is like regular arithmetic, but using binary rather than decimal numbers. In most computers, it is done with a fixed word size, with an extra bit to handle carry-over for exceeding it. See also BooleanLogic.

BinaryArithmetic is an example where simplification makes something very easy: Multiplication in decimal requires memorizing the times table, but in binary it is basically a copy. Example:

1. * 101001 = 37 * 41

--------------- -------


1. 148 (37*4=120+28)
   1. 37 (37*1)
      1. ----
         1. 1 <- carry
            1. 1517
               1. 1

---------------


1. <- carry
   1. = 1517

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CategoryMath