Multi-Stage Circuit Analysis

A B AND C D OR XOR Output

Question: If A=1, B=1, C=0, D=1, what is the output?

Answer: 0

Step 1: AND gate: A=1 AND B=1 → 1

Step 2: OR gate: C=0 OR D=1 → 1

Step 3: XOR gate: 1 XOR 1 → 0 (same values)

NOT → AND Circuit

A NOT B AND Output

Question: If A = 0 and B = 1, what is the output?

Answer: 1

Step 1: NOT gate converts A=0 to 1

Step 2: AND gate with 1 (from NOT) and B=1 gives 1

Logic Gates Review - Chapter 3
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⚡ Logic Gates Review

Chapter 3: Mastering Digital Logic

Let's review all 7 logic gates with correct symbols, truth tables, and circuit exercises!

AND Gate

Symbol

A B Y
Rule: Output is 1 ONLY when ALL inputs are 1

Truth Table

A B Output (Y)
0 0 0
0 1 0
1 0 0
1 1 1

OR Gate

Symbol

A B Y
Rule: Output is 1 when ANY input is 1

Truth Table

A B Output (Y)
0 0 0
0 1 1
1 0 1
1 1 1

NOT Gate

Symbol

A Y
Rule: Output is the OPPOSITE of input (inverts)

Truth Table

A Output (Y)
0 1
1 0

The small circle (○) means inversion!

NAND Gate

Symbol

A B Y
Rule: NOT + AND = Output is 0 ONLY when all inputs are 1

Truth Table

A B Output (Y)
0 0 1
0 1 1
1 0 1
1 1 0

Called the "Universal Gate" - can build any gate!

NOR Gate

Symbol

A B Y
Rule: NOT + OR = Output is 1 ONLY when all inputs are 0

Truth Table

A B Output (Y)
0 0 1
0 1 0
1 0 0
1 1 0

XOR Gate (Exclusive OR)

Symbol

A B Y
Rule: Output is 1 when inputs are DIFFERENT

Truth Table

A B Output (Y)
0 0 0
0 1 1
1 0 1
1 1 0

The extra curved line makes it exclusive!

XNOR Gate (Exclusive NOR)

Symbol

A B Y
Rule: Output is 1 when inputs are the SAME

Truth Table

A B Output (Y)
0 0 1
0 1 0
1 0 0
1 1 1

Also called the "Equality Checker"!

🎯 All 7 Gate Symbols

AND

All inputs = 1

OR

Any input = 1

NOT

Inverts input

XOR

Inputs different

NAND

NOT + AND

NOR

NOT + OR

XNOR

Inputs same

💡 Key Pattern: Circle (○) at the output = NOT operation added!

🔧 Circuit Exercise 1

Simple AND Circuit

A B AND Output

Question: If A = 1 and B = 0, what is the output?

Answer: 0

AND gate needs both inputs to be 1. Since B = 0, the output is 0.

Simple OR Circuit

A B OR Output

Question: If A = 0 and B = 0, what is the output?

Answer: 0

OR gate needs at least one input to be 1. Both are 0, so output is 0.

🔧 Circuit Exercise 2

NOT Gate Circuit

A NOT Output

Question: If A = 1, what is the output?

Answer: 0

NOT gate inverts: 1 becomes 0, 0 becomes 1.

XOR Gate Circuit

A B XOR Output

Question: If A = 1 and B = 1, what is the output?

Answer: 0

XOR outputs 1 only when inputs are different. Both are 1 (same), so output is 0.

🎯 NAND & NOR Challenge

NAND Gate Circuit

A B NAND Output

Question: If A = 1 and B = 1, what is the output?

Answer: 0

NAND is the opposite of AND. When both inputs are 1, AND would give 1, but NAND inverts it to 0.

NOR Gate Circuit

A B NOR Output

Question: If A = 0 and B = 0, what is the output?

Answer: 1

NOR outputs 1 only when all inputs are 0. Both inputs are 0, so output is 1!

⚡ Complex Circuit 1

Two-Stage Circuit: AND → OR

A B AND C OR Output

Question: If A = 1, B = 0, and C = 1, what is the output?

Answer: 1

Step 1: AND gate with A=1 and B=0 gives 0

Step 2: OR gate with 0 (from AND) and C=1 gives 1

⚡ Complex Circuit 2

NOT → AND Circuit

A ──→ [NOT] ──┐

├── [AND] ──→ Output

B ────────────┘

Question: If A = 0 and B = 1, what is the output?

Answer: 1

Step 1: NOT gate converts A=0 to 1

Step 2: AND gate with 1 (from NOT) and B=1 gives 1

⚡ Complex Circuit 3

XOR → NOT Circuit

A B XOR NOT Output

Question: If A = 1 and B = 0, what is the output?

Answer: 0

Step 1: XOR with A=1 and B=0 gives 1 (different)

Step 2: NOT gate inverts 1 to 0

Bonus: XOR → NOT is the same as XNOR!

🏆 Ultimate Challenge

Three-Stage Circuit

A B XOR C NOT AND Output

Question: If A = 1, B = 0, and C = 1, what is the final output?

Answer: 0

Step 1: XOR with A=1 and B=0 gives 1 (different)

Step 2: NOT converts C=1 to 0

Step 3: AND with 1 (XOR) and 0 (NOT) gives 0

🎨 Design Your Own Circuit

Challenge 1:

Build a circuit that outputs 1 only when exactly one input is 1, but not both.

Answer: Use an XOR gate!

A B XOR Output

Challenge 2:

Build a circuit that outputs 1 when both inputs are the same.

Answer: Use an XNOR gate!

A B XNOR Output

Challenge 3:

Build a circuit that always outputs the opposite of input A.

Answer: Use a NOT gate!

A NOT Output

🌍 Real-World Applications

🚗 Car Safety System

AND Gate: Car only starts when key is inserted AND seatbelt is fastened

🚨 Alarm System

OR Gate: Alarm triggers if door opens OR window breaks

💡 Smart Light Switch

XOR Gate: Light toggles when either of two switches changes state

🔐 Password Checker

XNOR Gate: Checks if entered password matches stored password

🔔 Doorbell System

NOT Gate: When button is NOT pressed, light is ON

🎮 Game Controller

Multiple Gates: Complex combinations of gates process button presses

💡 Every digital device you use is built using millions of these logic gates working together!

⚡ Quick Fire Quiz

1. Which gate is called the "universal gate"?

NAND gate - You can build any other gate using only NAND gates!

2. What does the small circle (○) on a gate symbol mean?

Inversion (NOT operation) - The output is inverted/flipped!

3. Which gate outputs 1 only when inputs are different?

XOR gate - Exclusive OR checks for difference!

4. How many rows are in a truth table for a 2-input gate?

4 rows - For n inputs, you need 2^n rows. With 2 inputs: 2² = 4 rows!

5. Which gate is also called the "Equality Checker"?

XNOR gate - It outputs 1 when both inputs are the same (equal)!

📝 Practice Worksheet

Fill in the outputs for this circuit:

A B OR NOT Output

Try all possible combinations:

Answers:

  • A=0, B=0 → OR gives 0, NOT gives 1
  • A=0, B=1 → OR gives 1, NOT gives 0
  • A=1, B=0 → OR gives 1, NOT gives 0
  • A=1, B=1 → OR gives 1, NOT gives 0

Bonus: This is actually a NOR gate!

🚀 Advanced Practice

Multi-Stage Circuit Analysis

A ──┐

├── [AND] ──┐

B ──┘ │

C ──┐ │

├── [OR] ───┤

D ──┘ │

├── [XOR] ──→ Output

│

Question: If A=1, B=1, C=0, D=1, what is the output?

Answer: 0

Step 1: AND gate: A=1 AND B=1 → 1

Step 2: OR gate: C=0 OR D=1 → 1

Step 3: XOR gate: 1 XOR 1 → 0 (same values)

📚 Chapter 3 Summary

The 7 Logic Gates:

  • AND - All inputs must be 1
  • OR - At least one input is 1
  • NOT - Inverts the input
  • XOR - Inputs must be different
  • NAND - NOT + AND (universal)
  • NOR - NOT + OR
  • XNOR - Inputs must be the same
🎯 Key Takeaway: Logic gates are the building blocks of all digital technology. By combining these simple gates, we can build complex circuits that power computers, smartphones, and all modern electronics!
💡 Remember: A circle (○) at the output means NOT operation is added!

🚀 Keep Practicing!

Ways to Master Logic Gates:

💡 Pro Tip: Try to build complex gates using only NAND or NOR gates. This is what real computer chips do!

🎉 Congratulations!

You've completed the Logic Gates Review for Chapter 3!

You now understand all 7 logic gates, their symbols, truth tables, and how to build complex circuits.

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