The fixed-point representation is a basic rule for data processing in computers. In fixed-point representation, which concerns integer numbers, the decimal point is always in the same position. The position of the decimal point is determined by the total number of digits and the number of digits written after the decimal point, the decimal places.
A fixed-point format can represent signed and unsigned integers and fractions. The difference between integer representation and fractional representation is only in the position of the binary comma. In integer representation, the comma is to the right of the number with the lowest significance, the Least Significant Bit( LSB). Fractional numbers, on the other hand, usually have their decimal point to the left of the sign bit.
For example, if the total number is seven and three decimal places are fixed, then there are four numbers before the decimal point and three after the decimal point. The digit sequence 1234567 becomes 1234.567 in this notation.
Machine words with 8, 16, 32 or 64 bits are used as representation units for fixed point numbers. The most significant bit( MSB) is used for the sign, the remaining binary digits for the digit representation. The computer performs the calculation as if the fixed point were located after the last binary digit of the machine word. In the case of a positive sign, it adds the individual dual values; in the case of a negative sign, it subtracts them.
Fixed point operations simplify numerical operations, they save memory, but require a compromise between dynamics and accuracy. The other representation form with floating decimal point is called floating point.