Decoders

Decoders are the combinational circuits that detect the presence of some code on its input and indicate the presence of that code by a specified output. Generally, a decoder has n input lines and 2n output lines.

n bit decoder block diagram

Basic binary decoder

Suppose we need to detect the occurrence of binary number 1100 on the input of the circuit. AND can be used as a decoding element because of AND gate produces HIGH output only when all of its inputs are HIGH. Now we have to make sure that all inputs to the AND gate are HIGH when the number 1100 occurs. This can be achieved by inverting last 2 bits. The corresponding circuit design and logic equations are shown in the figure.

binary decorder 1100 1

2-bit decoder

A 2-bit decoder (2 to 4-bit decoder) has 2 input lines and 4 output lines. That is, 4 decoding gates are required to decode all possible combinations of two bits. For any given code on its input, one of the four output becomes HIGH.

2 bit decoder block diagram

Binary codes corresponding outputs and decoding functions are described in the table.

Decimal DigitBinaryDecoding functionOutput
A0A10123
000{ \overline{A_0} \overline{A_1}}1000
101{\overline{A_0} A_1}0100
210{A_0 \overline{ A_1}}0010
311{A_0 A_1}0001

logical diagram of 2 to 4 bit decoder is shown in the figure.

2 bit decoder circuit

3-bit decoder

A 3-bit decoder has 3 input lines and 8 output lines. That is, 8 decoding gates are required to decode all possible combinations of three bits. For any given code on its input, one of the eight output becomes HIGH.

3 bit decoder block diagram

Binary codes corresponding outputs and decoding functions are described in the table.

Decimal DigitBinaryDecoding functionOutput
A2A1A001234567
0000{\overline{A_2} \overline{A_1} \overline{A_0}}10000000
1001{ \overline{A_2} \overline{A_1} A_0}01000000
2010{ \overline{A_2} A_1 \overline{ A_0}}00100000
3011{ \overline{A_2} A_1 A_0}00010000
4100{ A_2 \overline{A_1} \overline{ A_0}}00001000
5101{ A_2 \overline{A_1} A_0}00000100
6110{ A_2 A_1 \overline{A_0}}00000010
7111{ A_2 A_1 A_0}00000001

Circuit of a 3 bit decoder is given below,

3 bit decoder circuit

4-bit decoder

A 4-bit decoder has 4 input lines and 16 output lines. That is 16 decoding gates are required to decode all possible combinations of four bits. For any given code on its input, one of the sixteen output becomes HIGH.

4 bit decoder block diagram

Binary codes corresponding outputs and decoding functions are described in the table.

Decimal DigitBinaryDecoding functionOutput
A3A2A1A00123456789101112131415
00000{\overline{A_3} \overline{A_2} \overline{A_1} \overline{A_0}}1000000000000000
10001{\overline{A_3} \overline{A_2} \overline{A_1} A_0}0100000000000000
20010{\overline{A_3} \overline{A_2} A_1 \overline{ A_0}}0010000000000000
30011{\overline{A_3} \overline{A_2} A_1 A_0}0001000000000000
40100{\overline{A_3} A_2 \overline{A_1} \overline{ A_0}}0000100000000000
50101{\overline{A_3} A_2 \overline{A_1} A_0}0000010000000000
60110{\overline{A_3} A_2 A_1 \overline{A_0}}0000001000000000
70111{\overline{A_3} A_2 A_1 A_0}0000000100000000
81000{A_3 \overline{A_2} \overline{A_1} \overline{A_0}}0000000010000000
91001{A_3 \overline{A_2} \overline{A_1} A_0}0000000001000000
101010{A_3 \overline{A_2} A_1 \overline{A_0}}0000000000100000
111011{A_3 \overline{ A_2} A_1 A_0}0000000000010000
121100{A_3 A_2 \overline{A_1} \overline{A_0}}0000000000001000
131101{A_3 A_2 \overline{A_1} A_0}0000000000000100
141110{A_3 A_2 A_1 \overline{A_0}}0000000000000010
151111{A_3 A_2 A_1 A_0}0000000000000001

Click Here for Computer Organization and Architecture Malayalam Video Lessons

Further Reading

00vote
Article Rating
Subscribe
Notify of
guest
0 Comments
Inline Feedbacks
View all comments