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Multiplexer is a combinational circuit that has maximum of 2n data inputs, ‘n’ selection lines and single output line. One of these data inputs will be connected to the output based on the values of selection lines.

Since there are ‘n’ selection lines, there will be 2n possible combinations of zeros and ones. So, each combination will select only one data input. Multiplexer is also called as Mux.

4x1 Multiplexer

4x1 Multiplexer has four data inputs I3, I2, I1 & I0, two selection lines s1 & s0 and one output Y. The block diagram of 4x1 Multiplexer is shown in the following figure.

One of these 4 inputs will be connected to the output based on the combination of inputs present at these two selection lines. Truth table of 4x1 Multiplexer is shown below.


Selection LinesOutputS1S0Y00I001I110I211I3

From Truth table, we can directly write the Boolean function for output, Y as


We can implement this Boolean function using Inverters, AND gates & OR gate. The circuit diagram of 4x1 multiplexer is shown in the following figure.


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Binary to Gray code conversion

The Binary to Gray code converter is a logical circuit that is used to convert the binary code into its equivalent Gray code. By putting the MSB of 1 below the axis and the MSB of 1 above the axis and reflecting the (n-1) bit code about an axis after 2n-1 rows, we can obtain the n-bit gray code.

In 4-bit gray code, the 3-bit code is reflected against the axis drawn after the 24-1-1th =8th row.


Just like Binary to Gray code conversion; it is also a very simple process. There are the following steps used to convert the Gray code into binary.

  • Just like binary to gray, in gray to binary, the 1st bit of the binary number is similar to the MSB of the Gray code.
  • The 2nd bit of the binary number is the same as the 1st bit of the binary number when the 2nd bit of the Gray code is 0; otherwise, the 2nd bit is altered bit of the 1st bit of binary number. It means if the 1st bit of the binary is 1, then the 2nd bit is 0, and if it is 0, then the 2nd bit be 1.
  • The 2nd step continues for all the bits of the binary number.

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8x1 Multiplexer

In the 8 to 1 multiplexer, there are total eight inputs, i.e., A0, A1, A2, A3, A4, A5, A6, and A7, 3 selection lines, i.e., S0, S1and S2 and single output, i.e., Y. On the basis of the combination of inputs that are present at the selection lines S0, S1, and S2, one of these 8 inputs are connected to the output.

Let the 8x1 Multiplexer has eight data inputs I7 to I0, three selection lines s2, s1 & s0 and one output Y. The Truth table of 8x1 Multiplexer is shown below.

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