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.
Binary number only two possible outcomes of each partial multiplication: For example, the binary numbers 1011 and 1010 are multiplied as follows: Binary numbers can also be multiplied with bits after a binary point: See also Booth's multiplication algorithm. The binary multiplication table is the same as the truth table of the logical conjunction operation formula_6. Long division in binary is again similar to its decimal counterpart. In the example below, the divisor is 101, or 5 decimal, while the dividend is 11011, or 27 decimal. The procedure is the same as that of decimal long division; here, the divisor 101 goes