Introduction

Understanding the behavior of digital logic gates is crucial in circuit design and digital electronics. Two common logic gates are the NAND and NOR gates. This article delves into how connecting the inputs of a NAND gate and a NOR gate together can produce an XOR gate, a key component in digital circuits.

Understanding NAND and NOR Gates

Let's break down the operations of a NAND and a NOR gate and how their behavior differs.

NAND Gate

A NAND gate is a logical gate that outputs a LOW (0) only when both inputs are HIGH (1). Otherwise, the output is HIGH (1).

The truth table for a NAND gate is as follows:

A B NAND Output (A NAND B) 0 0 1 0 1 1 1 0 1 1 1 0

NOR Gate

A NOR gate outputs a HIGH (1) only when both inputs are LOW (0). Otherwise, the output is LOW (0).

The truth table for a NOR gate is as follows:

A B NOR Output (A NOR B) 0 0 1 0 1 0 1 0 0 1 1 0

Combining NAND and NOR Gates to Create XOR

To create an XOR gate, we connect the inputs of a NAND gate and a NOR gate together. This configuration draws from the unique properties of each gate to achieve the desired output.

Connecting Inputs of NAND and NOR Gates

When A and B are inputs to the NAND and NOR gates, the outputs can be analyzed as follows:

If both inputs are 0, the NAND output is 1 and the NOR output is 1. If one input is 1 and the other is 0, the NAND output is 1 and the NOR output is 0. If both inputs are 1, the NAND output is 0 and the NOR output is 0.

This composite output effectively mimics the behavior of an XOR gate, where the final output is HIGH (1) when the inputs are different (one is 0, the other is 1), and LOW (0) when the inputs are the same (both 0 or both 1).

Shorting Inputs of NAND and NOR Gates

Shorting the inputs of a NAND and NOR gate together produces a NOT gate. The output is the inverse of the input.

Using Extra Gates in IC Chips

In some cases, all inputs being tied together in a NAND or NOR gate makes the gate act as an inverter. This is useful when a circuit requires more inverters than available or when reusing gates from an IC with multiple identical gates.

For example, in the Apple II main logic board schematic, Wozniak used one gate of a 74LS02 2-input quad NOR gate chip with its inputs tied together to function as an inverter, feeding into the input of another NOR gate on the same IC package. This method is efficient and conserves components, allowing for a compact and cost-effective design.

This article has provided a detailed understanding of how NAND and NOR gates can be combined to create an XOR gate and the practical uses of tying inputs to produce NOT gates and saving components in IC chips.