lesson 7 .pdf

Lesson 7

1. Boolean Function Minimization


Presented by: Group 3
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2. What are
Functions?
•Reduces Hardware Cost → fewer gates, smaller circuits
•Improves Speed → less delay, faster response
•Saves Power → lower switching, energy-efficient
•Simplifies Design → easier to implement & debug
•Minimizes Space → compact chip layouts
•Enhances Reliability → fewer components, fewer failures
•Optimizes Tradeoff → balances cost, speed & power
•Supports CAD/EDA Tools → essential for FPGA & ASIC
design

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3. Introductio
n
Boolean function minimization =
process of reducing a Boolean
expression into its simplest form.
Goal: fewer logic gates, reduced
circuit cost, improved speed &
power efficiency.
Essential in digital electronics and
computer engineering.
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4. Boolean Algebra Simplification

F(A,B,C)=A′B+AB+BCF(A,B,C) = A'B + AB +
BCF(A,B,C)=A′B+AB+BC

Step 1: Factorize → F=B(A′+A)+BCF = B(A' + A) +
BCF=B(A′+A)+BC

Step 2: Apply Complement Law → F=B(1)+BCF = B(1) +
BCF=B(1)+BC

Step 3: Simplify → F=B+BCF = B + BCF=B+BC

Step 4: Absorption → F=BF = BF=B

Final Result: F=BF = BF=B

Example
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5. Karnaugh Map (K-map)

•A visual method for grouping minterms.
•Adjacent 1’s can be grouped in powers of
2 (1, 2, 4, 8...).
•Larger groups → simpler expression.

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6. Karnaugh Map (K-map)

Problem:
F(A,B,C,D)=Σ(0,2,5,7,8,10,13,15)F(A,B,C,D) = Σ
(0,2,5,7,8,10,13,15)F(A,B,C,D)=Σ(0,2,5,7,8,10,13,15)

Place 1’s in the K-map cells corresponding to minterms.
Group adjacent 1’s into largest possible blocks.
Derive simplified expression.
Diagram: 4-variable K-map with grouping

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7. Applications

Digital circuit design (simpler circuits).
Microprocessors & embedded systems.
VLSI chip design.
Compiler optimizations in logic synthesis.

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8. Conclusion
Algebraic → quick for small, simple functions.
K-map → best for medium-sized problems (3–6
variables).
Quine-McCluskey → systematic, scalable, used in
software tools for large circuits.


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9. Presented by;
GROUP 3
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7.1.5