Binary Subtraction Calculator

To accurately perform Binary Subtraction, input two Binary Numbers in calculator. Enter First Number (minuend) and Second Number (subtrahend) in their respective fields. The numbers should only contain 0s and 1s.

Click Calculate button to see Difference in both Binary and Decimal formats. The calculator will also show complete Step-by-Step Process including any Borrowing Operations.

How to Perform Binary Subtraction?

To perform Binary Subtraction, align Binary Numbers with their Rightmost Digits together. Start subtracting from Right to Left. When subtracting 1 from 0, borrow 1 from next Significant Bit, making current position 2 (10 in binary).

When Borrowing, a 1 becomes 0 in the digit borrowed from. The Subtraction Process follows Standard Rules while using only Binary Digits (0 and 1) with proper Borrowing Operations when needed.

Formula for Binary Subtraction

Basic Binary Subtraction Rules:

0 - 0 = 0 (No Borrowing)
1 - 0 = 1 (No Borrowing)
1 - 1 = 0 (No Borrowing)
0 - 1 = 1 (With Borrowing)

Borrowing Process:

When Borrowing Required:
Original Bit = 0, After Borrowing = 2 (10 in binary)
Lending Bit = 1, After Lending = 0

Binary to Decimal Conversion:

Decimal = Σ(Bit × 2^Position)
where:
Bit = Binary Digit (0 or 1)
Position = Position from right starting at 0

Decimal to Binary Conversion:

Binary = Quotient Remainder Sequence
where:
Quotient = Decimal Number ÷ 2 repeatedly
Remainder Sequence = Binary Digits from bottom to top

Example 1: Basic Subtraction

• First Number = 1010 (10 in decimal)
• Second Number = 0011 (3 in decimal)
• Process: 1010 – 0011
• Difference = 0111 (7 in decimal)
• Operation Type: No Borrowing Required

Example 2: With Borrowing

• First Number = 1000 (8 in decimal)
• Second Number = 0110 (6 in decimal)
• Process: 1000 – 0110
• Difference = 0010 (2 in decimal)
• Operation Type: Single Borrowing Required

Example 3: Complex Subtraction

• First Number = 10110 (22 in decimal)
• Second Number = 01011 (11 in decimal)
• Process: 10110 – 01011
• Difference = 01011 (11 in decimal)
• Operation Type: Multiple Borrowing Required

Example 4: Equal Numbers

• First Number = 1111 (15 in decimal)
• Second Number = 1111 (15 in decimal)
• Process: 1111 – 1111
• Difference = 0000 (0 in decimal)
• Operation Type: Simple Subtraction

Example 5: Large Numbers

• First Number = 11010 (26 in decimal)
• Second Number = 10001 (17 in decimal)
• Process: 11010 – 10001
• Difference = 01001 (9 in decimal)
• Operation Type: Multiple Borrowing Steps

What is Binary Subtraction?

Binary Subtraction is a fundamental Arithmetic Operation performed in Binary Number System, which uses only two digits (0 and 1). It follows similar principles to Decimal Subtraction but operates within the constraints of Binary Arithmetic. The operation involves a Minuend (number being subtracted from) and a Subtrahend (number being subtracted), resulting in a Difference. The process requires understanding of Binary Borrowing when Upper Digit is smaller than Lower Digit. This operation is essential for Computer Arithmetic, Digital Logic, and Binary Computations in modern Computing Systems.