Binary DecodersAn ninput binary decoder (Figure1.19) is a combinational system that has n binary inputs x = (x_{n1} , . . . , x_{0}) and 2^{n} binary outputs y = ( , . . . , y_{0}). The input vector x can be considered as representing integers from 0 to 2^{n}1 in the radix2 representation. When the input represents the integer i, then y_{i}, is equal to 1 and all other outputs are equal to 0. To facilitate the use of decoder modules in designing networks, an additional input, called module enable E, is provided. When E=0, all module outputs are 0 (or threestate).
Fig. 1.19  nInput binary decoder.
A highlevel description of an ninput binary decoder is
y_{i}=
 1 if x=i and E=1
 0 otherwise

where
and
In the description of systems that use this module, the decoder function is denoted by
y=DEC(x,E)
For example, DEC((l,l,0),l) = (0,1,0,0,0,0,0,0).
Fig. 1.20  Implementation of 2input binary decoder,(a) with getes and (b) with pass transistor.
The switching expressions that represent a binary decoder are
y_{i}=Em_{i}(x)
where, as defined in Chapter 3, m_{i}(x) is the ith minterm of the n variables x.
An implementation of a 2input binary decoder using gates is illustrated in Fig.1.20.a and a passtransistor implementation is shown in Figure 1.20.b. A binary decoder is used whenever a set of values has been encoded using a binary code and they have to be separated, that is, decoded. As an example, consider operation code in a computer. This code is part of every instruction and allies the operation to be executed.
Decoders exist for other representations of the input integer. For example, decimal decoders having ten outputs exist for codes such as BCD and Excess3. Their definition and implementation are similar to those of the binary decoder.
An Excess3 decoder has four inputs representing a decimal digit in the Excess3 code and ten outputs. The ith output is 1 when the input represents the integer i. The Excess3 code is given in the following table:
i
 X_{3}
 X_{2}
 X_{1}
 X_{0}



















































A highlevel description of the Excess3 decoder
Y=
 1 if x=i and 0 £ i £ 9
 0 otherwise

where
The switching expression for the ith output is
The design of ninput binary decoders using kinput binary decoders, k < n and the use of the binary decoder as a universal module are discussed in the following sections.
Date: 20150112; view: 1173
