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Two’s Complement

A numeric method for quantizing analog values into binary digital information. Though there are several different ways to quantize audio signals digitally, the numbering system known as “two’s complement” is often used because it allows for representation of negative and positive values in a form that makes further mathematical computations (such as adding positive and negative values together) easy to perform without introducing huge errors. It basically works by changing the value of the MSB between 0 (for positive numbers) and 1 (for negative numbers). If you were to look at a 16-bit binary signal the positive range goes from 0000000000000000 to 0111111111111111 (max positive signal). The negative range would go from 1111111111111111 (value just below zero) to 1000000000000000 (max negative value). So when the signal crosses zero all of the bits change from 0 to 1, or vice versa.

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