The quantization Q of a real-world value V is represented by a weighted sum of bits. Within the context of the general slope and bias encoding scheme, the value of an unsigned fixed-point quantity is given by
while the value of a signed fixed-point quantity is given by
are binary digits, with , for
The word size in bits is given by ws,
with ws =
S is given by , where the scaling is unrestricted because the binary point does not have to be contiguous with the word.
Formats for 8-bit signed and unsigned fixed-point values are shown in the following figure.
Note that you cannot discern whether these numbers are signed or unsigned data types merely by inspection since this information is not explicitly encoded within the word.
The binary number
0011.0101 yields the same
value for the unsigned and two's complement representation because
the MSB =
0. Setting B =
using the appropriate weights, bit multipliers, and scaling, the value
Conversely, the binary number
different values for the unsigned and two's complement representation
since the MSB =
Setting B =
0 and using
the appropriate weights, bit multipliers, and scaling, the unsigned
while the two's complement value is