442 Chapter 15
positive or negative number we can count to. The simple use of a sign bit leads to two values
for zero, which is not elegant or useful. One of the advantages of two’s complement coding
is that it makes subtraction simply a matter of addition. Arithmetic processes are at the heart
of digital signal processing and thus hold the key to handling digitized audio signals.
There are many advantages to be gained by handling analogue signals in digitized form
and, in no particular order, they include:
● great immunity from noise since the digitized signal can only be 1 or 0;
● exactly repeatable behavior;
● ability to correct for errors when they do occur;
● simple arithmetic operations, very easy for computers;Table 15.1 : Four-Bit Binary Number Coding Methods
Binary number representation
Decimal number Sign plus magnitude Two’s complement Offset binary
7 0011 0111 1111
6 0110 0110 1110
5 0101 0101 1101
4 0100 0100 1100
3 0011 0011 1011
2 0010 0010 1010
1 0001 0001 1001
0 0000 0000 1000
0 1000 (0000) (1000)
1 1001 1111 0111
2 1010 1110 0110
3 1011 1101 0101
4 1100 1100 0100
5 1101 1011 0011
6 1110 1010 0010
7 1111 1001 0001
8 1000 0000