Binary Calculator
Perform arithmetic operations (add, subtract, multiply, divide) on binary numbers. An essential tool for computer science students and professionals.
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The Beginner's Guide to Binary Arithmetic
The binary number system is the backbone of all modern computers. It uses only two digits, 0 and 1, to represent all data. While humans use the decimal (base-10) system, computers use binary (base-2). This calculator allows you to perform basic arithmetic operations—addition, subtraction, multiplication, and division—directly on binary numbers.
Understanding Binary Numbers
In the decimal system, each digit's position represents a power of 10 (1s, 10s, 100s, etc.). In binary, each position represents a power of 2 (1s, 2s, 4s, 8s, 16s, etc.).
For example, the binary number 1011 is converted to decimal as follows:
- (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
- (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
- 8 + 0 + 2 + 1 = 11 in decimal.
Binary Arithmetic Rules
Binary arithmetic follows specific rules, which this calculator automates.
Binary Addition
The rules are simple, but involve "carrying over," just like in decimal addition.
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0, carry over 1 to the next column
Binary Subtraction
Subtraction can involve "borrowing" from the next column.
- 0 - 0 = 0
- 1 - 0 = 1
- 1 - 1 = 0
- 0 - 1 = 1, borrow 1 from the next column
Binary Multiplication
Multiplication is similar to decimal long multiplication, but simpler because you only multiply by 0 or 1.
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
Binary Division
Binary division is similar to decimal long division. You check if the divisor "fits" into the dividend, and if it does, you place a 1 in the quotient.
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