---
title: "Positive/negative logic; Ex-NOR using NOR"
subject: "Digital Logic"
chapter: 2
key: "semester_3/digital_logic:positive-negative-logic-xnor-nor"
source: https://www.bctengineer.com/q/semester_3/digital_logic/positive-negative-logic-xnor-nor
site: BCT Engineering
---

# Positive/negative logic; Ex-NOR using NOR

Digital Logic · Chapter 2: Digital Logic

- Asked in: 2080 Baisakh, 2+3 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/positive-negative-logic-xnor-nor
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-2

## Question

Describe positive and negative logic with an example. Construct Ex-NOR gate using only NOR gates.

## Short answer

Positive logic uses HIGH=1, LOW=0; negative logic uses HIGH=0, LOW=1. The same physical gate becomes AND in positive logic but OR in negative logic. Ex-NOR (XNOR) can be built with four NOR gates: compute (A+B)′, then (A+(A+B)′)′ and (B+(A+B)′)′, and NOR these to get A⊙B.

## Answer

#### Positive and negative logic
- **Positive logic:** HIGH voltage = 1, LOW voltage = 0. Example: TTL with +5 V = 1, 0 V = 0.
- **Negative logic:** HIGH voltage = 0, LOW voltage = 1. Example: +5 V = 0, 0 V = 1.

**Example:** a gate gives a HIGH output only when both inputs are HIGH (L L → L, L H → L, H L → L, H H → H).
- In positive logic this is 00→0, 01→0, 10→0, 11→1: an **AND** gate.
- In negative logic this is 11→1, 10→1, 01→1, 00→0: an **OR** gate.

So positive AND = negative OR (and positive NAND = negative NOR, positive XOR = negative XNOR).

#### Ex-NOR gate using only NOR gates
$Y = A \odot B = AB + \bar A \bar B = \overline{A\bar B + \bar A B}$ needs **four 2-input NOR gates** (the dual of the 4-NAND XOR).

$$
\begin{aligned} G_1 &= \overline{A + B} \\ G_2 &= \overline{A + G_1} = \bar A (A + B) = \bar A B \\ G_3 &= \overline{B + G_1} = \bar B (A + B) = A \bar B \\ Y &= \overline{G_2 + G_3} = \overline{\bar A B + A \bar B} = A \odot B \end{aligned}
$$

```text
 A --+---------------[NOR G2]--+
     |                 |       |
     +--[NOR G1]---G1--+       +--[NOR G4]-- Y
     |                 |       |
 B --+---------------[NOR G3]--+
```

| A | B | $G_1$ | $G_2$ | $G_3$ | Y |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 |

## Check yourself

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

1. A gate with HIGH output only when both inputs HIGH is, in negative logic:
   A. AND
   B. NOR
   C. OR
   D. XOR
   Answer: C. Its negative-logic table is 11->1,10->1,01->1,00->0, an OR. (Key point: Example gate)

2. Positive NAND equals negative:
   A. AND
   B. XOR
   C. NAND
   D. NOR
   Answer: D. Complementing all bits converts NAND to NOR. (Key point: Equivalences)

3. Gates used in NOR-only XNOR:
   A. Four 2-input NOR
   B. Two NOR
   C. Five NOR
   D. Three NOR
   Answer: A. Dual of the 4-NAND XOR. (Key point: XNOR gates)

4. G3 = NOR(B, G1) equals:
   A. A'B
   B. A B'
   C. A'B'
   D. AB
   Answer: B. G3 = B'(A+B) = AB'. (Key point: G3)

## Close variants set in other exams

- [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×

## Related in Digital Logic

- [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
- [3-input XNOR using NOR gates only](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Athree-input-xnor-nor) — Digital Logic, chapter 2
- [F = (A+B)(C+D)E using NOR gates only](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Anor-only-function-realize) — Digital Logic, chapter 2
- [2-input XOR using NOR gates only](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Axor-using-nor-only) — Digital Logic, chapter 2, asked 2×
- [De Morgan; positive NAND equals negative NOR](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademorgan-positive-nand-negative-nor) — Digital Logic, chapter 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×

## Related in other subjects

- [Short note: Ex-OR and Ex-NOR gate](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Ashort-note-xor-xnor) — Basic Electrical and Electronics Engineering, chapter 3
- [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