Logic gates | CEE Academy

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LOGIC GATES

▢ Analogue and Digital Signals:

Table 1: Analogue vs Digital

Term	Meaning	Example
Analogue signal	Continuously varying voltage/current signal	Sinusoidally varying alternating voltage
Analogue circuit	Circuit associated with analogue signal	AC signal circuit
Digital signal	Signal having only two discrete values	Square wave
Digital circuit	Electronic circuit handling only digital signal	Logic circuit

▢ Logic Gate:

❖ Definition: Digital circuit with one or more input signals but only one output signal

❖ Gate: Digital switch that can be closed/opened to pass or stop digital signal

❖ Logic Gate Condition: Gate opens to pass digital signal only when required logical condition is satisfied

Table 1: Binary States

Binary digit	Meaning
1	ON, true, yes, closed, high
0	OFF, false, no, open, low

❖ Truth Table: Table showing all possible input-output combinations of a logic gate

▢ Boolean Algebra:

❖ Definition: Algebra based on logical states used to describe logic circuits

❖ Boolean Variables: Logical statements represented by 1 and 0

❖ Fundamental Laws:

•
OR law
•
AND law
•
NOT law

Table 1: Basic Boolean Operations

Law	Symbol	Meaning
OR	+
AND	.
NOT	bar

▢ Boolean Algebra Laws:

Table 1: Basic Laws

Law	Formula
Commutative law of OR	\(A+B=B+A\)
Commutative law of AND	\(A.B=B.A\)
Associative law of OR	\(A+(B+C)=(A+B)+C\)
Associative law of AND	\(A.(B.C)=(A.B).C\)
Distributive law	\(A.(B+C)=A.B+A.C\)
OR identity	\(A+0=A\)
OR domination	\(A+1=1\)
OR idempotent	\(A+A=A\)
OR complement	\(A+\bar A=1\)
AND zero	\(A.0=0\)
AND identity	\(A.1=A\)
AND idempotent	\(A.A=A\)
AND complement	\(A.\bar A=0\)
Double complement	\(\bar{\bar A}=A\)
Absorption law	\(A+A.B=A\)
Absorption law	\(A.(A+B)=A\)
Special identity	\(\bar A+A.B=\bar A+B\)
Special identity	\(A.(\bar A+B)=A.B\)

▢ De Morgan's Theorem:

Table 1: De Morgan Laws

Statement	Formula
Complement of sum = product of complements	\(\overline{A+B}=\bar A.\bar B\)
Complement of product = sum of complements	\(\overline{A.B}=\bar A+\bar B\)

▢ Basic Logic Gates:

❖ Types:

•
OR gate
•
AND gate
•
NOT gate

▢ OR Gate:

❖ Definition: Logic gate with two or more inputs and one output; output is 1 if any input is 1

❖ Boolean Expression: \(Y=A+B\)

❖ Switching Equivalent: Parallel switching circuit

Table 1: OR Gate Truth Table

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	1

▢ AND Gate:

❖ Definition: Logic gate with two or more inputs and one output; output is 1 only if all inputs are 1

❖ Boolean Expression: \(Y=A.B\)

❖ Switching Equivalent: Series switching circuit

Table 1: AND Gate Truth Table

A	B	Y
0	0	0
0	1	0
1	0	0
1	1	1

▢ NOT Gate:

❖ Definition: Logic gate with one input and one output; output is complement of input

❖ Boolean Expression: \(Y=\bar A\)

❖ Also Called: Inverter

❖ Input Terminal: Only one input terminal

Table 1: NOT Gate Truth Table

A	Y
0	1
1	0

▢ Combination Gates:

❖ Types:

•
NOR gate
•
NAND gate
•
XOR gate
•
XNOR gate

▢ NOR Gate:

❖ Full Form: NOT + OR

❖ Definition: Output of OR gate is connected to input of NOT gate

❖ Boolean Expression: \(Y=\overline{A+B}\)

❖ Also Called: Inverter gate

Table 1: NOR Gate Truth Table

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	0

❖ Universal Gate: Yes

▢ NAND Gate:

❖ Full Form: NOT + AND

❖ Definition: Output of AND gate is connected to input of NOT gate

❖ Boolean Expression: \(Y=\overline{A.B}\)

Table 1: NAND Gate Truth Table

A	B	Y
0	0	1
0	1	1
1	0	1
1	1	0

❖ Universal Gate: Yes

▢ XOR Gate:

❖ Full Form: Exclusive OR gate

❖ Definition: Output is 1 only when inputs are different

❖ Boolean Expression: \(Y=A.\bar B+\bar A.B\)

❖ Alternative Expression: \(Y=(A+B).\overline{A.B}\)

Table 1: XOR Gate Truth Table

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	0

▢ XNOR Gate:

❖ Full Form: Exclusive NOR gate

❖ Definition: Output is 1 only when inputs are same

❖ Boolean Expression: \(Y=A.B+\bar A.\bar B\)

❖ Relation: XNOR is inverse of XOR gate

Table 1: XNOR Gate Truth Table

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	1

▢ Universal Gates:

Table 1: Universal Gate Facts

Fact	Answer
Universal gates	NAND and NOR
Building blocks of digital circuit	NAND and NOR
Reason	All other gates can be made using NAND or NOR
Digital circuit construction	Can be made by repeated use of NAND gates
NOR gate	Also called inverter gate

▢ Gate Switching Equivalents:

Table 1: Switching Equivalents

Gate	Equivalent circuit
AND	Series switching circuit
OR	Parallel switching circuit
NOT	One input terminal

▢ Read and Digest:

Table 1: Important Points

Fact	Answer
Binary system	Number system using only 0 and 1
Boolean expression	Obeys commutative, associative and distributive laws
OR gate	Output 1 if any input is 1
AND gate	Output 1 only if all inputs are 1
NOT gate	Output is complement of input
NAND gate	AND followed by NOT
NOR gate	OR followed by NOT
XOR gate	Output 1 when inputs are unequal
XNOR gate	Output 1 when inputs are equal
NAND and NOR	Universal gates
NAND and NOR	Building blocks of digital circuit
Digital signal	Only two discrete values
Truth table	All input-output combinations

▢ Objective Answer Key:

Table 1: Logic Gates MCQ Answers

Q	Ans
1	a
2	a
3	b
4	c
5	a
6	b
7	b
8	b
9	d
10	c
11	a
12	c
13	a
14	c
15	b
16	c

▢ High-Yield Recall:

Table 1: Logic Gates One-Liners

Fact	Answer
Analogue signal	Continuously varying signal
Digital signal	Two discrete values
Binary digits	0 and 1
Logic gate	One/more inputs, one output
Truth table	Input-output possibility table
OR expression	\(Y=A+B\)
AND expression	\(Y=A.B\)
NOT expression	\(Y=\bar A\)
NOR expression	\(Y=\overline{A+B}\)
NAND expression	\(Y=\overline{A.B}\)
XOR expression	\(Y=A.\bar B+\bar A.B\)
XNOR expression	\(Y=A.B+\bar A.\bar B\)
AND equivalent	Series switching
OR equivalent	Parallel switching
Universal gates	NAND and NOR
De Morgan 1	\(\overline{A+B}=\bar A.\bar B\)
De Morgan 2	\(\overline{A.B}=\bar A+\bar B\)
AND output 1	Only when all inputs are 1
OR output 0	Only when all inputs are 0
XOR output 1	Inputs different
XNOR output 1	Inputs same

Q1.

NAND gate gives low output when

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Q2.

Which of the following is universal gate?

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Q3.

Which of the following gates can be used in the construction of digital circuit?

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Q4.

Which of the following is an invert gate?

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Q5.

NOR gate functions as:

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Q6.

Which of the following act as a universal gate?

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Q7.

If NAND gate is short circuited then it forms:

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Q8.

Which of the following is universal gate?

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Q9.

Which of the following can act as the building blocks for the other gates?

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Q10.

Combination of gates shown in the following figure is:

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Q11.

The given truth table is of which logic gate?

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Q12.

The output in the following logic circuit is:

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Q13.

The following table is truth table of:

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Q14.

The truth table for NOT gate is:

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Q15.

What is the value of \(A+\bar A\) in the Boolean algebra?

Q16.

What is the Boolean expression for the gate circuit shown in Fig.?

Q17.

Identify the gate represented by the block diagram.

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Q18.

The only function of a NOR gate is to:

Q19.

NAND gate is a combination of:

Q20.

Two inputs of NAND gates are shorted. This gate is equivalent to:

Q21.

What is the name of the gate obtained by the combination shown in the figure?

Q22.

Two NOR gates are connected at the two inputs of a NAND gate. This combination will behave like:

Q23.