GCE (A/L) ICT | UNIVERSAL LOGIC GATES | UNIT 04 English Tamil Medium Online Class Notes

UNIT 4 – DIGITAL CIRCUITS (Beginner Friendly Notes)

Digital circuits are the foundation of computers and electronic devices. They work using only two values:

• 0 – OFF / FALSE / No electricity
• 1 – ON / TRUE / Electricity present

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(i) LOGIC GATES

A logic gate is an electronic component that takes one or more binary inputs (0 or 1) and produces a binary output.

1. AND Gate

Rule: Output is 1 only if all inputs are 1.

A	B	A · B
0	0	0
0	1	0
1	0	0
1	1	1

Real-life example: You can enter a room only if you have an ID card AND permission.

2. OR Gate

Rule: Output is 1 if at least one input is 1.

A	B	A + B
0	0	0
0	1	1
1	0	1
1	1	1

3. NOT Gate

Rule: Output is the opposite of the input.

A	Ā
0	1
1	0

4. NAND Gate

Rule: Output is the opposite of AND gate.

NAND gate gives output 0 only when both inputs are 1.

5. NOR Gate

Rule: Output is the opposite of OR gate.

NOR gate gives output 1 only when both inputs are 0.

6. XOR Gate

Rule: Output is 1 when inputs are different.

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	0

7. XNOR Gate

Rule: Output is 1 when inputs are same.

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Universal Gates

NAND and NOR are called Universal Gates because all other logic gates can be created using only NAND gates or only NOR gates.

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(ii) BOOLEAN ALGEBRA

Boolean Algebra is a mathematical method used to analyze and simplify digital circuits.

Basic Boolean Laws

• A + A = A
• A · A = A
• A + 1 = 1
• A · 0 = 0
• A + Ā = 1
• A · Ā = 0

De Morgan’s Laws

• (A · B)̅ = Ā + B̅
• (A + B)̅ = Ā · B̅

SOP and POS

SOP (Sum of Products): AND operations first, then OR.

Example: A·B + C·D

POS (Product of Sums): OR operations first, then AND.

Example: (A + B)(C + D)

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(iii) DESIGNING LOGIC CIRCUITS

Boolean expressions can be converted into logic circuits using gates.

Example: Y = (A + B) · C

• A + B → OR gate
• Output AND with C
• Final output is Y

Truth tables are used to verify the correctness of circuits.

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(iv) CPU AND MEMORY (RAM)

Half Adder

A Half Adder adds two binary bits.

A	B	Sum	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Sum is generated using XOR gate and Carry using AND gate.

Full Adder

A Full Adder adds three bits: A, B and Carry-in. It is used in the Arithmetic Logic Unit (ALU) of the CPU.

Memory and Flip-Flops

Memory circuits store data using feedback loops.

Flip-Flop: A basic memory unit capable of storing 1 bit of data.

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Boolean Algebra Laws – Step by Step for Beginners

Boolean algebra works with only two values:

• 1 = TRUE (ON)
• 0 = FALSE (OFF)

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1. Commutative Law

Changing the order does not change the result.

A · B = B · A

A + B = B + A

2. Associative Law

Changing the grouping does not change the result.

A · (B · C) = (A · B) · C

A + (B + C) = (A + B) + C

3. Idempotent Law

Repeating the same variable has no effect.

A · A = A

A + A = A

4. Double Negative Law

Opposite of opposite gives original value.

Ā̄ = A

5. Complementary Law

A · Ā = 0

A + Ā = 1

6. Intersection Law

A · 1 = A

A · 0 = 0

7. Union Law

A + 1 = 1

A + 0 = A

8. Distributive Law

A · (B + C) = (A · B) + (A · C)

A + (B · C) = (A + B) · (A + C)

9. Absorption Law

A · (A + B) = A

A + (A · B) = A

10. Redundancy Law

A · (Ā + B) = A · B

A + (Ā + B) = A + B

11. De Morgan’s Law

(A · B)̄ = Ā + B̄

(A + B)̄ = Ā · B̄

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PART 1: BOOLEAN ALGEBRA – STEP-BY-STEP FOR BEGINNERS

First: Basic Meaning (Very Important)

Symbol	Meaning	Example
1	TRUE / ON	Light is ON
0	FALSE / OFF	Light is OFF
A, B	Inputs	Switches
A · B	AND	Both ON
A + B	OR	Any one ON
Ā	NOT A	Opposite of A

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1. Commutative Law

Meaning: Order does NOT change the result

AND Example

• A = 1, B = 0

• A · B = 1 · 0 = 0

• B · A = 0 · 1 = 0

✅ Same answer → Order does not matter

OR Example

• A = 1, B = 0

• A + B = 1 + 0 = 1

• B + A = 0 + 1 = 1

✔️ Law proven

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2. Associative Law

Meaning: Grouping does NOT matter

AND Example

Let A=1, B=1, C=0

Step 1:

A · (B · C)
= 1 · (1 · 0)
= 1 · 0
= 0

Step 2:

(A · B) · C
= (1 · 1) · 0
= 1 · 0
= 0

✔️ Same result

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3. Idempotent Law

Meaning: Repeating same value changes nothing

Example

A = 1 → A · A = 1 · 1 = 1
A = 0 → A + A = 0 + 0 = 0

So:

• A · A = A

• A + A = A

✔️ No effect by repetition

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4. Double Negative Law

Meaning: Opposite of opposite = original

Example:

• A = 1 → Ā = 0 → Ā̄ = 1

• A = 0 → Ā = 1 → Ā̄ = 0

✔️ Ā̄ = A

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5. Complementary Law

Meaning: A and NOT A

AND Case

A · Ā
= 1 · 0 = 0
= 0 · 1 = 0

Always FALSE

OR Case

A + Ā
= 1 + 0 = 1
= 0 + 1 = 1

Always TRUE

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6. Intersection Law (AND with constants)

Example

A · 1 = A
A · 0 = 0

Think:

• AND with TRUE → keeps value

• AND with FALSE → always FALSE

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7. Union Law (OR with constants)

Example

A + 1 = 1
A + 0 = A

Think:

• OR with TRUE → always TRUE

• OR with FALSE → keeps value

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8. Distributive Law

Meaning: Like normal algebra

Example 1

A · (B + C)
= A · B + A · C

Let A=1, B=0, C=1

Left:

1 · (0 + 1)
= 1 · 1
= 1

Right:

(1 · 0) + (1 · 1)
= 0 + 1
= 1

✔️ Works

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9. Absorption Law

Meaning: Extra part is useless

Example

A · (A + B)

If A=1:

1 · (1 + B) = 1

If A=0:

0 · (0 + B) = 0

✔️ Always A

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10. Redundancy Law

Meaning: Remove unnecessary terms

Example:

A · (Ā + B)

Since:

• A · Ā = 0

So:

A · B

✔️ Simpler form

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11. De Morgan’s Law (VERY IMPORTANT)

Rule:

• NOT moves inside

• AND ↔ OR (swap)

• Each variable gets NOT

Example 1

(A · B)̄ = Ā + B̄

Example 2

(A + B)̄ = Ā · B̄

Used heavily in logic circuits & exams.

Tip: These laws are essential for simplifying digital logic circuits.

Conclusion: Logic gates form circuits, circuits form processors, and processors make computers work.