MONOGRAPH

LOGIC GATES

COMPILED:2026-10-23

Logic Gates

Tags: #◇Computer Science #◇CSARCH1 #◇Conceptual #◇M3

◇Overview

This sub-module discusses the logic gates used in digital systems.
Objective: Learn the different logic gates used in digital logic systems.

◇Key Definitions

Logic Gates & Boolean Expressions

Logic gates are tools for expressing a given Boolean expression in a symbolic format.
A Boolean expression is an equation in which the result will either be a 0 or 1.
A Boolean function (logic function) is an expression formed with binary variables, binary or unary operators, parentheses, and an equal sign. Example: $F= \bar{X}\bar{Y}Z + X\bar{Y}\bar{Z}$ .
1 value means "True", "Correct", High, 5-volts.
0 value means "False", "Incorrect", Low, 0-volt.

◇Theoretical Framework: Gate Types

AND Gate

Function: "All or nothing" gate; outputs true only if ALL inputs are true. (Switches in series)
Expression: $Y = A \cdot B$

OR Gate

Function: "Any or all" gate; outputs true if at least one input is true. (Switches in parallel)
Expression: $Y = A + B$

NOT Gate (Inverter)

Function: Negates the input expression. Can only have one input at a time.
Expression: $Y = A'$

Buffer Gate

Function: Transfer gate used to delay the output. Does not negate. Can only have one input.
Expression: $Y = A$

NAND Gate

Function: Complement of the AND gate. Outputs false only if all inputs are true.
Expression: $Y = (A \cdot B)'$

NOR Gate

Function: Complement of the OR gate. Outputs true only if all inputs are false.
Expression: $Y = (A + B)'$

XOR (Exclusive-OR) Gate

Function: Odd function; outputs true if the input variables have an odd number of binary 1's.
Expression: $Y = A \oplus B = A'B + AB'$

XNOR (Equivalence) Gate

Function: Even function; outputs true if the input variables have an even number of binary 0's (or identical inputs for 2 variables).
Expression: $Y = (A \oplus B)' = AB + A'B'$

Truth Table

Represents a Boolean function showing the output for all possible input combinations.
The number of rows is $2^n$ where $n$ is the number of variables.

Previous Topic: ◇Boolean Algebra
Next Topic: ◇Karnaugh Map
Related Notes: ◇Boolean Algebra, ◇Combinational Circuit - Design

CONFIRMATION // 理解度の確認

ACTIVE RECALL VERIFICATION

Select an answer to verify conceptual comprehension and reveal the technical rationale.

Q1

What does a 1 value typically represent in a digital logic system?

Q2

Which gate is known as the "all or nothing" gate because it only outputs true if ALL inputs are true?

Q3

How is the OR gate often referred to?

Q4

What is the primary function of a NOT gate?

Q5

A Buffer gate is primarily used for what purpose?

Q6

Which gate is the exact complement of the AND gate?

Q7

The NOR gate outputs a true condition ONLY under what circumstance?

Q8

Which gate outputs a true condition if the input variables have an odd number of binary 1s?

Q9

The XNOR gate is also known by what other name?

Q10

How many rows are required in a truth table for a logic circuit with 'n' input variables?

Logic Gates | PROJECT ENGRAM