Decoder

Decoder is a combinational circuit that has ‘n’ input lines and maximum of 2n output lines. One of these outputs will be active High based on the combination of inputs present, when the decoder is enabled. That means decoder detects a particular code. The outputs of the decoder are nothing but the min terms of ‘n’ input variables lines, when it is enabled.

2 to 4 Decoder

Let 2 to 4 Decoder has two inputs A1 & A0 and four outputs Y3, Y2, Y1 & Y0. The block diagram of 2 to 4 decoder is shown in the following figure.

One of these four outputs will be ‘1’ for each combination of inputs when enable, E is ‘1’. The Truth table of 2 to 4 decoder is shown below.

Enable	Inputs		Outputs
E	A1	A0	Y3	Y2	Y1	Y0
0	x	x	0	0	0	0
1	0	0	0	0	0	1
1	0	1	0	0	1	0
1	1	0	0	1	0	0
1	1	1	1	0	0	0

From Truth table, we can write the Boolean functions for each output as.

Y3=E.A1.A0

Y2=E.A1.A0′

Y1=E.A1′.A0

Y0=E.A1′.A0′

The product phrase for each output is unique. Thus, there are a total of four product phrases. Four AND gates with three inputs each and two inverters can be used to implement these four product phrases. In the figure below, you can see the circuit diagram for the 2 to 4 decoder.

Therefore, the outputs of 2 to 4 decoder are nothing but the min terms of two input variables A1 & A0, when enable, E is equal to one. If enable, E is zero, then all the outputs of decoder will be equal to zero.

Similarly, 3 to 8 decoder produces eight min terms of three input variables A2, A1 & A0 and 4 to 16 decoder produces sixteen min terms of four input variables A3, A2, A1 & A0.