Second Semester_Digital Logic_Combinational Circuit Design

Second Semester_Digital Logic_Combinational Circuit Design

September 06, 2025

4.1 Half Adder, Full Adder, Half Subtractor, Full Subtractor

Half Adder: Adds two bits (A + B).
- Outputs: Sum = A ⊕ B, Carry = A·B
Full Adder: Adds three bits (A + B + Cin).
- Outputs: Sum = A ⊕ B ⊕ Cin, Carry = (A·B) + (B·Cin) + (A·Cin)
Half Subtractor: Subtracts two bits (A − B).
- Outputs: Difference = A ⊕ B, Borrow = A'·B
Full Subtractor: Subtracts three bits (A − B − Bin).
- Outputs: Difference = A ⊕ B ⊕ Bin, Borrow = A'·B + (A'⊕B)·Bin

4.2 Code Converters

Convert one code to another in digital systems.
Common types:
- Binary to Gray and Gray to Binary
- BCD to Excess-3
- Binary to ASCII

4.3 Multiplexers (MUX) and Demultiplexers (DEMUX)

Multiplexer: Selects one input from many and sends it to output.
- Controlled by select lines.
- Example: 4-to-1 MUX has 4 inputs, 1 output, 2 select lines.
Demultiplexer: Takes one input and routes it to one of many outputs.
- Controlled by select lines.

4.4 Encoders and Decoders

Encoder: Converts 2ⁿ inputs into n-bit code (e.g., 8-to-3 encoder).
Decoder: Converts n-bit code into 2ⁿ outputs (e.g., 3-to-8 decoder).
Applications: Memory addressing, code conversion, data routing.

4.5 Combinational Circuit Design Procedure

Define inputs, outputs, and function.
Create truth table.
Derive logic expression (Sum of Products / Product of Sums).
Simplify using Boolean algebra or K-map.
Draw logic diagram using gates.
Verify with truth table or simulation.

4.6 Binary Parallel Adder

Adds two n-bit binary numbers in parallel using n full adders.
Carry propagates from least significant bit (LSB) to most significant bit (MSB).
Faster designs: Carry Look-Ahead Adder (CLA) to reduce delay.

4.7 Decimal Adder

Adds two decimal numbers in BCD (Binary-Coded Decimal) format.
Uses 4-bit BCD adders and correction logic to handle sums > 9.
Output: Correct BCD result with proper carry to next decimal digit.

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