Fundamentals - The MPEG - page 49

Figure 2.42: Structure of fast multiplier: the input A is multiplied by 1, 2, 4, 8, etc., by bit shifting. The digits of the B
input then determine which multiples of A should be added together by enabling AND gates between the shifters
and the adder. For long wordlengths, the number of gates required becomes enormous, and the device is best
implemented in a chip.
In a given application, all that matters is that the output has the correct numerical value. It does not matter if this is
achieved using dedicated hardware or using software in a general-purpose processor. It should be clear that if it is
wished to simulate analog gain control in the digital domain by multiplication, the samples to be multiplied must
have been uniformly quantized. If the quantizing is non-uniform the binary numbers are no longer proportional to
the original parameter and multiplication will not give the correct result.
In audio, uniform quantizing is universal in production systems. However, in video it is not owing to the widespread
use of gamma which will be discussed in Chapter 6 . Strictly speaking, video signals with gamma should be
returned to the uniformly quantized domain before processing but this is seldom done in practice.
2.19 Floating-point coding
Computers operate on data words of fixed length and if binary or two's complement coding is used, this limits the
range of the numbers. For this reason many computers use floating-point coding which allows a much greater
range of numbers with a penalty of reduced accuracy.
Figure 2.43 (a) shows that in pure binary, numbers which are significantly below the full scale value have a number
of high-order bits which are all zero. Instead of handling these bits individually, as they are all zero it is good
enough simply to count them. Figure 2.43 (b) shows that every time a leading zero is removed, the remaining bits
are shifted left one place and this has the effect in binary of multiplying by two. Two shifts multiply by four, three
shifts by eight and so on. In order to re- create the number with the right magnitude, the power of two by which the
number was multiplied must also be sent. This value is known as the exponent .