Decoders can detect a code and activate a single output to signal the presence of that code. Decoders have many applications, from producing system alerts in alarm systems to performing the task of driving multiple devices in microprocessor systems (e.g. memory).

Basic Binary Decoder

The function of the binary decoder is to determine if a given input combination has occurred. For example, if we wish to detect that 1011 occurs on the inputs of a digital circuit we must design a decoder which only outputs ‘1’ for this instance. Accordingly, a 4-input AND gate and an Inverter may be employed as illustrated in Figure 2-7.

Figure 2-7 Decoding circuit for X=1011

The Three Bit Binary Decoder

In order to decode all possible combinations of three bits, eight (2³=8) decoding logic gates are required. This type of decoder is called the 3-line-to-8-line decoder because they are 3 inputs and 8 outputs. Let us consider the design of such a decoder and assume that we require ACTIVE HIGH outputs. That is, for a given input combination the decoder outputs ‘1’. To illustrate lets consider Table 2-11 which list the decoding functions and truth tables for the 3-line-to-8-line decoder.

Decimal Digit	Binary Inputs			Logic Function	Outputs
					D0	D1	D2	D3	D4	D5	D6	D7
0	0	0	0		1	0	0	0	0	0	0	0
1	0	0	1		0	1	0	0	0	0	0	0
2	0	1	0		0	0	1	0	0	0	0	0
3	0	1	1		0	0	0	1	0	0	0	0
4	1	0	0		0	0	0	0	1	0	0	0
5	1	0	1		0	0	0	0	0	1	0	0
6	1	1	0		0	0	0	0	0	0	1	0
7	1	1	1		0	0	0	0	0	0	0	1

Table 2-11 Decoding functions and truth tables for the 3-line-to-8-line decoder

 

Now, we can develop a decoder based on each logic function and implement the SOP logic circuit. This is illustrated below in Figure 2-8.

Figure 2-8 Internal Circuitry for 3-line-to-8-line decoder

It is far more convenient to use the logic symbol for the3-line-to-8-line decoder as illustrated in Figure 2-9 rather than repeating the complex internal circuitry each time. 

 

Figure 2-9 Logic Symbol for 3-line-to-8-line decoder

Note the 3-line-to-8-line is sometimes referred to as the 3 x 8 decoder

 

The BCD-to-Decimal Decoder

 

The BCD-to-decimal decoder converts each BCD code to its decimal equivalent. The technique employed is very similar to the one used in developing the 3-line-to-8-line decoder. Again assuming active high outputs are required, Table 2-12 lists the decoding functions for BCD-to-decimal decoder

 

Decimal Digit	Binary Inputs				Logic Function
0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	0	0	0
6	1	0	0	1

Table 2-12 Decoding functions for the BCD-to-decimal decoder

Now, we can develop a decoder based on each logic function and implement the SOP logic circuit. This is illustrated below in Figure 2-10.

Figure 2-10 Logic Circuit for BCD decoder

 

 

Copyright © Adrian Als , 1999
This page was last modified: Wednesday, April 12, 2000