Design an 8-input to 3-output decoder using NAND gates only. Draw the logic diagram.

Q.) Design an 8-input to 3-output decoder using NAND gates only. Draw the logic diagram.

 Subject: Digital Systems

A decoder is a combinational circuit that converts binary information from n coded inputs to a maximum of 2^n unique outputs. They are used in a wide variety of applications, including data multiplexing and data demultiplexing, seven segment displays, and memory address decoding.

An 8-input to 3-output decoder will have 8 inputs (2^3 = 8) and 3 outputs. The outputs are usually active low, meaning they go low when selected.

To design an 8-input to 3-output decoder using NAND gates only, we first need to understand that a NAND gate is a universal gate, meaning any logic function can be implemented using only NAND gates.

The truth table for a 3-to-8 decoder is as follows:

Inputs Outputs
A B C D0 D1 D2 D3 D4 D5 D6 D7
0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
1 1 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1

The logic diagram for the 3-to-8 decoder using NAND gates only is a bit complex and cannot be drawn here due to the limitations of the text-based format. However, I can describe how to draw it:

  1. First, draw three input lines labeled A, B, and C.
  2. Draw eight output lines labeled D0 to D7.
  3. Connect each output to a NAND gate. The inputs of these NAND gates will be connected to the A, B, and C lines in various combinations of NOT gates and direct connections.
  4. For D0, connect the inputs of the NAND gate to A, B, and C through NOT gates.
  5. For D1, connect the first input to A through a NOT gate, and connect the second and third inputs directly to B and C.
  6. Continue this pattern for the remaining outputs, changing the combination of NOT gates and direct connections according to the truth table.

Remember, the output of a NAND gate is low only when all its inputs are high. So, for each output, connect the inputs of the NAND gate in such a way that they will all be high when the corresponding input combination is applied.

This logic diagram will implement an 8-input to 3-output decoder using NAND gates only.