Logarithmic number system Logarithmic number system A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. In an LNS, a number, formula_1, is represented by the logarithm, formula_2, of its absolute value as follows: where formula_4 is a bit denoting the sign of formula_1 (formula_6 if formula_7 and formula_8 if formula_9). The number formula_2 is represented by a binary word which usually is in the two's complement format. An LNS can be considered as a floating-point number with the significand being always equal to 1 and a non-integer exponent.
Skew binary number system with formula_8 1s is equal to the binary number formula_9 minus formula_8. Let formula_11 represents the digit formula_12 repeated formula_13 times. The skew binary number of the form formula_14 with formula_8 1s is equal to the binary number formula_16 minus formula_8. Similarly to the preceding section, the binary number formula_18 of the form formula_7 with formula_8 1s equals the skew binary number formula_21 plus formula_8. Note that since addition is not defined, adding formula_8 corresponds to incrementing the number formula_8 times. However, formula_8 is bounded by the logarithm of formula_18 and incrementation takes constant time. Hence transforming a binary number