---
title: "Universal gates; positive and negative logic"
subject: "Digital Logic"
chapter: 2
key: "semester_3/digital_logic:universal-gates-positive-logic"
source: https://www.bctengineer.com/q/semester_3/digital_logic/universal-gates-positive-logic
site: BCT Engineering
---

# Universal gates; positive and negative logic

Digital Logic · Chapter 2: Digital Logic

- Asked in: 2078 Kartik, 2+2 marks
- Video: [Positive and Negative Logic](https://www.youtube.com/watch?v=gtucOKD1pHA) — Neso Academy
- 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-positive-logic
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-2

## Question

Define universal gates with example. Explain positive and negative logic.

## Short answer

Universal gates like NAND and NOR can realize any Boolean function. For instance, NAND alone builds NOT, AND, OR. Positive logic assigns HIGH=1, LOW=0; negative logic reverses. Because of this convention change, a gate’s logical function changes: positive AND becomes negative OR, positive NAND becomes negative NOR.

## Answer

#### Universal gates
A **universal gate** is a gate that alone can implement NOT, AND and OR, and hence any Boolean function. **NAND** and **NOR** are universal gates.

Examples with NAND only:
- NOT: $\overline{A \cdot A} = \bar A$
- AND: NAND followed by a NAND inverter, $\overline{\overline{AB}} = AB$
- OR: $\overline{\bar A \cdot \bar B} = A + B$

Examples with NOR only:
- NOT: $\overline{A + A} = \bar A$
- OR: NOR followed by a NOR inverter
- AND: $\overline{\bar A + \bar B} = AB$

```text
 OR from NAND:
 A --[NAND]-- A' --+
 B --[NAND]-- B' --+--[NAND]-- A+B
```

#### Positive and negative logic
- **Positive logic:** HIGH level = logic 1 and LOW level = logic 0 (e.g. +5 V = 1, 0 V = 0).
- **Negative logic:** HIGH level = logic 0 and LOW level = logic 1.

The same circuit changes its logic name when the convention changes. A gate with output HIGH only when both inputs are HIGH is AND in positive logic but OR in negative logic; similarly positive NAND = negative NOR.

## Check yourself

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

1. A universal gate can alone implement:
   A. Only NOT
   B. Only AND
   C. NOT, AND and OR
   D. Only memory
   Answer: C. Hence any Boolean function. (Key point: Definition)

2. OR from NAND is:
   A. NAND of A and B
   B. NAND of A and B'
   C. NAND of 0 and 1
   D. NAND of A' and B'
   Answer: D. (A'B')' = A+B. (Key point: NAND OR)

3. NOT using NOR:
   A. NOR with both inputs tied to A
   B. NOR of A and 1
   C. NOR of A and B
   D. NOR of A and A'
   Answer: A. (A+A)' = A'. (Key point: NOR NOT)

4. Positive NAND corresponds to negative:
   A. AND
   B. NOR
   C. OR
   D. XNOR
   Answer: B. Switching conventions complements all bits. (Key point: Logic change)

## Related in Digital Logic

- [Positive/negative logic; XNOR using NAND](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Apositive-negative-logic-xnor-nand) — Digital Logic, chapter 2, asked 2×
- [Positive/negative logic; Ex-NOR using NOR](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Apositive-negative-logic-xnor-nor) — Digital Logic, chapter 2, asked 2×
- [Positive and negative logic](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Apositive-negative-logic) — Digital Logic, chapter 2, asked 2×
- [Positive/negative logic; verify 3-variable De Morgan](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-three-variable-verify) — 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
- [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

## 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
- [Short note: Logic gates](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Ashort-note-logic-gates) — Basic Electrical and Electronics Engineering, chapter 3
- [Effective mass can be positive or negative](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aeffective-mass-positive-negative) — Electrical Engineering Material, chapter 1, asked 4×
- [Short note: Positive and negative feedback](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Ashort-note-feedback) — Basic Electronics Engineering, chapter 4