---
title: "Why NOR and NAND are universal gates"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:universal-gates-nor-nand"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/universal-gates-nor-nand
site: BCT Engineering
---

# Why NOR and NAND are universal gates

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2067 Chaitra, 3 marks
- Video: [Why NAND & NOR is called as universal gates | Universal Gates | Digital Electronics](https://www.youtube.com/watch?v=qwQeQmyZ7WM) — iFocus Institute
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/universal-gates-nor-nand
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Why NOR and NAND gates are called universal gates? Explain with examples.

## Short answer

NAND and NOR gates are universal because NOT, AND, and OR—hence any logic function—can be built using only one gate type. For example, a NOT is made by tying both inputs of a NAND (or NOR); AND is NAND followed by NOT; OR is NOR followed by NOT.

## Answer

NAND and NOR gates are called **universal gates** because any logic function (AND, OR, NOT, and hence any combination) can be built using only NAND gates, or only NOR gates.

#### NAND gate as universal gate

| Function | Using NAND only |
|---|---|
| NOT | A' = (A·A)' (tie both inputs) |
| AND | AB = ((AB)')' (NAND followed by NAND as NOT) |
| OR | A + B = (A'·B')' (NAND of A' and B') |

```text
 NOT:  A --[NAND, inputs tied]-- A'
 AND:  A,B --[NAND]--[NAND tied]-- AB
 OR:   A --[NAND tied]--+
       B --[NAND tied]--[NAND]-- A+B
```

#### NOR gate as universal gate

| Function | Using NOR only |
|---|---|
| NOT | A' = (A + A)' |
| OR | A + B = ((A + B)')' (NOR followed by NOR as NOT) |
| AND | AB = (A' + B')' (NOR of A' and B') |

Example: to make an OR gate from NOR gates, connect the output of a NOR gate to a second NOR gate with tied inputs.

Because NOT, AND and OR are enough to build every logic circuit, NAND and NOR are universal. They are also cheaper and smaller in ICs, which is why they are widely used.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. NAND and NOR are called universal gates because:
   A. Any logic function can be built using only NAND or only NOR
   B. They have only one input
   C. They are the cheapest gates
   D. They need no power
   Answer: A. The answer states this: Any logic function can be built using only NAND or only NOR. (Key point: Meaning of universal)

2. A NOT gate is made from a NAND gate by:
   A. Leaving one input open
   B. Tying both inputs together
   C. Adding a NOR gate
   D. Using three inputs
   Answer: B. The answer states this: Tying both inputs together. (Key point: NOT from NAND)

3. A + B using NAND gates equals:
   A. NAND of A and B
   B. NAND followed by NOT of A
   C. NAND of A' and B'
   D. A' . B'
   Answer: C. The answer states this: NAND of A' and B'. (Key point: OR from NAND)

4. AB using NOR gates equals:
   A. NOR of A and B
   B. NOR of A and B'
   C. A' + B'
   D. NOR of A' and B'
   Answer: D. The answer states this: NOR of A' and B'. (Key point: AND from NOR)

## Related in Basic Electronics Engineering

- [X-OR gate using NAND gates only](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Axor-using-nand) — Basic Electronics Engineering, chapter 6
- [Encoder; NAND and XOR truth tables](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aencoder-truth-tables) — Basic Electronics Engineering, chapter 6
- [2's complement subtraction; AND using NOR](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-111-110-nor-and) — Basic Electronics Engineering, chapter 6

## Related in other subjects

- [Why NAND and NOR are universal gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Auniversal-gates-why) — Digital Logic, chapter 2
- [Universal gates; Ex-OR using NAND](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Auniversal-gates-xor-nand) — Digital Logic, chapter 2
- [De Morgan; NOR gate from NAND gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-importance-nor-from-nand) — Digital Logic, chapter 2
- [Universal motor and why so called](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Auniversal-motor-construction-operation) — Electrical Machine, chapter 7