1.4 Decoder
1-out-of-n decoder
A 1-out-of-n decoder is a circuit with n outputs and ld n inputs. Outputs yJ are numbered from 0 to (n — 1). An output therefore goes to "one" precisely when the input binary number A is identical to the number J of the relevant output. Figure 1.16 shows the truth table for a l-out-of-4 decoder. The variables a0 and al represent the straight binary code of the number A. The sum of the products (disjunctive normal- form) of the receding functions can be taken directly from the truth table. Figure 1.17 shows the corresponding implementation.
A |
a1 |
a2 |
y3 |
y2 |
y1 |
y0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
2 |
1 |
0 |
0 |
1 |
0 |
0 |
3 |
1 |
1 |
1 |
0 |
0 |
0 |
Fig.
1.16 -
Truth table of a l-out-of-4 decoder.
Fig.
1.17 - Circuit
of a l-out-of-4 decoder.
When using monolithic integrated circuits, hand functions are often chosen rather than and functions, so that most of the output variables are complemented (barred).
Types of 1C: TTL CMOS
10 outputs 74LS42 4028
For further 1C types, see the following section on demultiplexers.
Priority decoder
The 1-out-of-n code can be converted to straight binary code by using a priority decoder. At its outputs a straight binary number appears which corresponds to the highest input number which is logic 1. The value of the lower-index input variables is irrelevant, hence the name priority decoder. This property enables the circuit to convert not only the 1-out-of-n code but also a sum code in which not just one variable is 1, but also all the less significant bits. The truth table of the priority decoder is shown in Fig.1.18.
J |
X9 |
X8 |
X7 |
X6 |
X5 |
X4 |
X3 |
X2 |
X1 |
Y3 |
Y2 |
Y1 |
Y0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
X |
0 |
0 |
1 |
0 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
X |
X |
0 |
0 |
1 |
1 |
4 |
0 |
0 |
0 |
0 |
0 |
1 |
X |
X |
X |
0 |
1 |
0 |
0 |
5 |
0 |
0 |
0 |
0 |
1 |
X |
X |
X |
X |
0 |
1 |
0 |
1 |
6 |
0 |
0 |
0 |
1 |
X |
X |
X |
X |
X |
0 |
1 |
1 |
0 |
7 |
0 |
0 |
1 |
X |
X |
X |
X |
X |
X |
0 |
1 |
1 |
1 |
8 |
0 |
1 |
X |
X |
X |
X |
X |
X |
X |
1 |
0 |
0 |
0 |
9 |
1 |
X |
X |
X |
X |
X |
X |
X |
X |
1 |
0 |
0 |
1 |
Fig. 1.18 - Truth table of a priority decoder, x = any.
1C types:
l-out-of-10 code: SN 74147 (TTL) MC 10165 (ECL);
l-out-of-8 code, extendable: SN 74148 (TTL); MC14532(CMOS)