Full Subtractor & Half Subtractor Calculator

What are Half Subtractors and Full Subtractors?

Half subtractors and full subtractors are fundamental digital circuits that perform binary subtraction. They complement adders in arithmetic logic units (ALUs) and are essential for complete arithmetic operations in digital systems.

How to Use This Calculator

1. Select subtractor type - Choose between Half Subtractor (2 inputs) or Full Subtractor (3 inputs)
2. Set input values - Check boxes to set inputs to 1 (unchecked = 0)
3. Click "Calculate" to compute difference and borrow outputs
4. View results including truth table and Boolean expressions
5. Copy or export the analysis for your projects

Understanding Half Subtractors

What is a Half Subtractor?

A half subtractor is a digital circuit that subtracts one binary digit from another. It produces two outputs: Difference and Borrow. The "half" designation indicates it cannot handle a borrow input from a previous subtraction stage.

Half Subtractor Truth Table

A	B	Difference	Borrow
0	0	0	0
0	1	1	1
1	0	1	0
1	1	0	0

Half Subtractor Boolean Expressions

• Difference = A ⊕ B (XOR operation)
• Borrow = ¬A · B (NOT A AND B)

Understanding Full Subtractors

What is a Full Subtractor?

A full subtractor subtracts two binary digits and accounts for a borrow from the previous stage. This makes it suitable for multi-bit binary subtraction where borrow propagation is essential.

Full Subtractor Boolean Expressions

• Difference = A ⊕ B ⊕ Bin (XOR of all three inputs)
• Borrow = ¬A·B + ¬A·Bin + B·Bin (Borrow generation logic)

Applications and Uses

Arithmetic Logic Units (ALUs)

Subtractors work alongside adders in ALUs to provide:

• Integer subtraction operations
• Comparison operations (A - B to check equality)
• Two's complement arithmetic
• Address offset calculations

Digital System Applications

• Down counters and timers
• Digital signal processing
• Error detection circuits
• Magnitude comparators

Examples & Worked Problems

Example 1: Half Subtractor

Problem: Subtract 1 - 0

Solution:

• A = 1, B = 0
• Difference = 1 ⊕ 0 = 1
• Borrow = ¬1 · 0 = 0
• Result: 1₂ (no borrow needed)

Example 2: Half Subtractor with Borrow

Problem: Subtract 0 - 1

Solution:

• A = 0, B = 1
• Difference = 0 ⊕ 1 = 1
• Borrow = ¬0 · 1 = 1
• Result: 1₂ with borrow (represents -1 in two's complement)

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