---
title: "Why NAND and NOR are universal gates"
subject: "Digital Logic"
chapter: 2
key: "semester_3/digital_logic:universal-gates-why"
source: https://www.bctengineer.com/q/semester_3/digital_logic/universal-gates-why
site: BCT Engineering
---

# Why NAND and NOR are universal gates

Digital Logic · Chapter 2: Digital Logic

- Asked in: 2068 Baisakh, 4 marks
- Video: [Lec-4: Implement all Gates using NAND & NOR Gate | Why NAND & NOR are called Universal Gates](https://www.youtube.com/watch?v=w2hK0JVKmJc) — Gate Smashers
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/universal-gates-why
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-2

## Question

Why NAND and NOR gates are called Universal gates? Illustrate with examples.

## Short answer

NAND and NOR are universal because each can implement NOT, AND, and OR. Examples: NAND (A A) = A', (A NAND B) NAND (A NAND B) = AB, (A NAND A) NAND (B NAND B) = A+B. Thus any Boolean function can be built with only one type.

## Answer

**NAND and NOR gates are called universal gates** because each of them alone can realise the three basic operations NOT, AND and OR, and therefore any Boolean function. A complete circuit can thus be made using only one type of gate (e.g. 7400 quad NAND or 7402 quad NOR), which reduces inventory, cost and design effort.

#### Using NAND only
| Gate | Realisation | Gates |
|---|---|---|
| NOT | $\overline{A \cdot A} = \bar A$ | 1 |
| AND | $\overline{\overline{AB} \cdot \overline{AB}} = AB$ | 2 |
| OR | $\overline{\bar A \cdot \bar B} = A + B$ | 3 |

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

#### Using NOR only
| Gate | Realisation | Gates |
|---|---|---|
| NOT | $\overline{A + A} = \bar A$ | 1 |
| OR | $\overline{\overline{A+B} + \overline{A+B}} = A + B$ | 2 |
| AND | $\overline{\bar A + \bar B} = AB$ | 3 |

```text
 NOT: A --[NOR]-- A'
 OR : A,B --[NOR]--[NOR]-- A+B
 AND: A --[NOR]-- A' --+
      B --[NOR]-- B' --+--[NOR]-- AB
```

**Example:** $Y = AB + CD$ can be done with three NAND gates: $Y = \overline{\overline{AB} \cdot \overline{CD}}$ (NAND-NAND form of an SOP).

## Check yourself

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

1. A universal gate is one that:
   A. Has the most inputs
   B. Is used only in memories
   C. Gives output 1 always
   D. Alone can realise NOT, AND and OR
   Answer: D. Since NOT, AND, OR are realisable, any function can be built. (Key point: Definition)

2. How is AND made from NAND gates?
   A. NAND followed by a NAND inverter (2 gates)
   B. One NAND gate
   C. Three NAND gates with inverted inputs
   D. NAND of A and B'
   Answer: A. (AB)' inverted by a tied-input NAND gives AB. (Key point: NAND AND)

3. How is AND made from NOR gates?
   A. NOR of A and B
   B. NOR of A' and B' (3 gates)
   C. Single NOR with tied inputs
   D. NOR followed by one NOR inverter
   Answer: B. (A'+B')' = AB, needing two inverters plus one NOR. (Key point: NOR AND)

4. What is a practical benefit of using universal gates?
   A. Lower propagation delay always
   B. No power consumption
   C. One IC type (e.g. 7400) can build the whole circuit, reducing cost
   D. Fewer gates always
   Answer: C. Using one IC type reduces inventory, cost and design effort. (Key point: Practical benefit)

## Related in Digital Logic

- [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 gates; positive and negative logic](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Auniversal-gates-positive-logic) — Digital Logic, chapter 2
- [Minterms/maxterms; K-map Σm(2,4,5,13,14)+d, universal gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aminterm-maxterm-kmap-universal) — Digital Logic, chapter 3
- [De Morgan; X-NOR using a universal gate](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-xnor-universal-gate) — Digital Logic, chapter 2
- [XOR gate using minimum NAND gates](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Axor-using-nand-only) — Digital Logic, chapter 2, asked 2×

## Related in other subjects

- [Why NOR and NAND are universal gates](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Auniversal-gates-nor-nand) — Basic Electronics Engineering, chapter 6
- [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
- [CMOS NAND, NOR (and NOT) circuits](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Acmos-nand-nor-circuits) — Embedded System, chapter 8, asked 2×
- [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