Circuit Design

Circuit design brings together all the topics in this course: logic gates, Boolean algebra, truth tables, K-maps, adders, and flip-flops. In OCR H446, you need to be able to design circuits from requirements, combine gates effectively, minimise before implementing, and understand real-world applications of digital circuit design.

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The Circuit Design Process

Step	Action	Tools used
1	Understand the requirements	Problem description, input/output specification
2	Construct the truth table	List all input combinations and desired outputs
3	Derive the Boolean expression	Sum of Products (minterms) from the truth table
4	Simplify the expression	Boolean algebra laws, K-maps
5	Draw the circuit	Logic gate symbols
6	Verify the circuit	Trace through with test inputs

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Worked Example 1: Majority Vote Circuit

Requirement: Design a circuit with three inputs (A, B, C) that outputs 1 when at least two of the three inputs are 1.

Step 1: Truth table:

A	B	C	Q
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1

Step 2: Sum of Products: Q = (NOT A AND B AND C) OR (A AND NOT B AND C) OR (A AND B AND NOT C) OR (A AND B AND C)

Step 3: Simplify using K-map:

	BC=00	BC=01	BC=11	BC=10
A=0	0	0	1	0
A=1	0	1	1	1

Groups:

• Group 1 (A=1, BC=01 and A=1, BC=11): A AND C (2 cells)
• Group 2 (A=0, BC=11 and A=1, BC=11): B AND C (2 cells)
• Group 3 (A=1, BC=11 and A=1, BC=10): A AND B (2 cells)

Simplified expression: Q = (A AND B) OR (A AND C) OR (B AND C)

Step 4: Circuit:

A ---+---+
     |   |
B ---+---|---+
     |   |   |
C ---|---+---+
     |   |   |
     AND AND AND
     |   |   |
     AB  AC  BC
      \  |  /
       \ | /
        OR
         |
         Q

Three AND gates and one 3-input OR gate. Total: 4 gates.

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Worked Example 2: Alarm System

Requirement: An alarm sounds (Q=1) when:

• The system is armed (A=1), AND
• Either the door sensor (D=1) OR the window sensor (W=1) is triggered

Expression: Q = A AND (D OR W)

Truth table:

A	D	W	D OR W	Q = A AND (D OR W)
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	1	0
1	0	0	0	0
1	0	1	1	1
1	1	0	1	1
1	1	1	1	1

Circuit: One OR gate (inputs D, W) feeding into one AND gate (with A). Only 2 gates needed.

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Minimisation Before Implementation

Why minimise?

Factor	Before minimisation	After minimisation
Gate count	Higher	Lower
Cost	More expensive	Cheaper
Power	Higher consumption	Lower consumption
Speed	More delays (more levels)	Fewer delays (fewer levels)
Reliability	More components to fail	Fewer potential failure points
PCB area	Larger board needed	Smaller board

Methods of minimisation:

1. Boolean algebra — algebraic simplification using laws
2. Karnaugh maps — visual grouping for 2-4 variables
3. Quine-McCluskey algorithm — systematic method for any number of variables (beyond OCR spec but worth knowing exists)

Exam Tip: Always simplify before drawing a circuit. Unsimplified circuits will work but will not earn full marks if the question asks for a "minimised" or "simplified" design.

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Worked Example 3: 7-Segment Display Decoder (Segment a)

A 7-segment display shows digits 0-9 using segments labelled a to g. Let us design the circuit for segment 'a' (the top horizontal segment).

Segment 'a' is ON for digits: 0, 2, 3, 5, 6, 7, 8, 9. Segment 'a' is OFF for digits: 1, 4.

Using 4-bit BCD input (A B C D where A is MSB):