3-input AND gate using 4:1 mux

As we know, a AND gate's output goes '1' when all its inputs are '1', otherwise it is '0'. The truth table for a 3-input AND gate is shown below in figure 1, where A, B and C are the three inputs and O is the output.

                                      O = A (and) B (and) C

Truth table for 3-input AND gate

A 4:1 mux has 2 select lines. We can connect A and B to each of the select lines. The output will, then, be a function of the third input C. Now, if we sub-partition the truth table for distinct values of A and B, we observe

When A = 0 and B = 0, O = 0 => Connect D0 pin of mux to '0'

When A = 0 and B = 1, O = 0 => Connect D1 pin of mux to '0'

When A = 1 and B = 0, O = 0 => Connect D2 pin of mux to '0'

When A = 1 and B = 1, O = C => Connect D3 pin of mux to C

The implementation of 3-input AND gate, based upon our discussion so far, is as shown in figure 2 below:

Also read:

• XOR gate implementation using NAND gates
• 16x1 mux using 4x1 muxes
• 2-inputs gates using 2:1 mux
• 3-input AND gate using 2:1 muxes

3-input XOR gate using 2-input XOR gates

A 3-input XOR gate can be implemented using 2-input XOR gates by cascading 2 2-input XOR gates. Two of the three inputs will feed one of the 2-input XOR gates. The output of the first gate will, then, be XORed with the third input to get the final output.

Let us say, we want to XOR three inputs A,B and C to get the output Z. First, XOR A and B together to obtain intermediate output Y. Then XOR Y and C to obtain Z. The schematic representation to obtain 3-input XOR gate by cascading 2-input XOR gates is shown in figure below:

Implementation of 3-input XOR gate using 2-input XOR gates