# Binary Numbers

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0 and 1. These are the only two symbols available in a binary counting system. The reason binary numbers dominate electronics is that these numbers correspond to off and on, false and true, switch open and switch closed, magnetized in one direction, magnetized in the other, light x-polarized or light y-polarized. Any more complicated idea can be made by aggregating multiple binary bits

(1 bit = a single 0 or 1) in assemblies: nybbles (4 bits), bytes (8 bits), words (16 bits), or long words (32 bits).

Place value works for binary just as it does for the decimal system. In ordinary decimal numbers 234 means 2×100 + 3×10 + 4×1 or 2×10^{2} + 3×10^{1} + 4×10^{0}. Each place has a digit in the range 0 through 9 times the base of the number system (10) raised to an integer power. If we looked at real numbers, those including a decimal point, numbers past the decimal would feature the base raised to a negative power. ANY based raised to the 0 power is 1. The position immediately to the left of base0 is valued at base1 which for binary means 2^{1} = 2. So the first few binary numbers are: 00, 01, 10, 11 which correspond to the base 10 numbers 0, 1, 2, and 3.