4-Bit Binary Subtractor Using Logic Gates

A 4-bit binary subtractor designed and implemented using logic gates in Logisim.

Overview

This project implements a 4-bit binary subtractor using four cascaded Full Subtractors in a ripple-borrow configuration.

The circuit takes two 4-bit binary inputs and produces:

• A 4-bit difference
• A final borrow output

Tools Used

• Logisim 2.7.1
• Digital logic gates

Circuit Architecture

Each Full Subtractor is constructed using:

• Two Half Subtractors
• One OR gate

Four Full Subtractors are then cascaded. The borrow output from each stage is connected to the borrow input of the next higher-order stage.

Full Subtractor Equations

Difference:

D = A XOR B XOR Bin

Borrow output:

Bout = B1 OR B2

where:

• B1 = NOT(A) AND B
• B2 = NOT(D1) AND Bin

4-Bit Borrow Propagation

The borrow propagates as follows:

Bin0 → FS0 → FS1 → FS2 → FS3 → Bout

The initial borrow input is set to 0.

Inputs and Outputs

Inputs

• A[3:0]
• B[3:0]
• Initial borrow input = 0

Outputs

• D[3:0]
• Bout

For unsigned subtraction, a final borrow of 1 indicates that A is smaller than B.

Testing

A	B	Expected Difference	Expected Bout
0101	0011	0010	0
0101	0101	0000	0
0111	0010	0101	0
0011	0101	1110	1
0000	0001	1111	1
0000	0000	0000	0

Files

• 4-Bit_Binary_Subtractor.circ — Editable Logisim circuit
• circuit.png — Final circuit diagram
• truth-tables.png — Half and Full Subtractor truth tables
• testing-results.png — Testing documentation
• project-report.pdf — Project report

Learning Outcomes

Through this project, I strengthened my understanding of:

• Logic gates
• Boolean expressions
• Half and Full Subtractors
• Binary arithmetic
• Ripple-borrow propagation
• Digital circuit simulation
• Circuit testing and debugging

Author

Deep Das
B.Tech ECE Student at Delhi Technological University (DTU)

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