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A base is the number of different symbols used to represent a number in a single digit. For example, we mostly use base-10 (decimal), which represents each of the numbers that can go in a single digit, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. However, there can be times that other bases may be useful. Computers do calculations in base-2, also known as binary. The circuits of computers know 2 levels of voltage, high and low. These can be represented using the numbers 0 for low and 1 for high.Binary and OctalSince binary is important in the use of computers, that makes the multiples of 2 important as well. They become important because they become other ways to represent a select number of binary digits. I will use base-4 or quaternary for an example. When using quaternary, 2 binary digits can be represented with 1 quaternary digit. 012 = 14 102 = 24 112 = 34 OctalYou can take this one digit further by using base-8, or octal. 0012 = 18 0102 = 28 0112 = 38 1002 = 48 1012 = 58 1102 = 68 1112 = 78 HexadecimalThe next base is the most commonly used base for programmers, base-16 or hexadecimal (note: many use X as a symbol for hexadecimal). For this base, one must go beyond the ten numbers commonly used. Six more symbols are needed. Those who first started using hexadecimal chose the first six letters of the alphabet, A, B, C, D, E, and F. You can think of A as the equivalent of 10, B=11, .... 00012 = 1X 00102 = 2X 00112 = 3X 01002 = 4X 01012 = 5X 01102 = 6X 01112 = 7X 10002 = 8X 10012 = 9X 10102 = AX 10112 = BX 11002 = CX 11012 = DX 11102 = EX 11112 = FX 011010010011100110010101000111012 = 6939951BX |
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