BINARY NUMBER PRECISION AND DYNAMIC RANGE
As we implied earlier, for any binary number format, the number of bits in a data word is a key consideration. The more bits used in the word, the better the resolution of the number, and the larger the maximum value that can be represented.[
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When 2b is much larger than 1, we can ignore the –1 in Eq. (12-6) and state that
Equation 12-6'
Equation (12-6'), dimensioned in dB, tells us that the dynamic range of our number system is directly proportional to the word length. Thus, an eight-bit two's complement word, with seven bits available to represent signal magnitude, has a dynamic range of 6.02 · 7 = 42.14 dB. Most people simplify Eq. (12-6') by using the rule of thumb that the dynamic range is equal to "six dB per bit."
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