Binary Calculator
Perform binary arithmetic operations with step-by-step explanations
Binary Arithmetic Calculator
Number of bits for result representation
Only 0s and 1s allowed
Only 0s and 1s allowed
Example Calculations
Binary Addition
1101 (13)
+ 1010 (10)
------
10111 (23)
Binary Multiplication
101 (5)
× 11 (3)
------
1111 (15)
Binary Operation Rules
Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (carry 1)
Multiplication
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
Binary to Decimal
0001=1
0010=2
0011=3
0100=4
0101=5
1000=8
1111=15
Binary Calculator Tips
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Binary uses only digits 0 and 1
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Each position represents a power of 2
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Watch for overflow in fixed-width operations
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Negative numbers use two's complement
Understanding Binary Arithmetic
What is Binary?
Binary is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from 2⁰ on the right.
Why Use Binary?
- •Computers use binary for digital logic
- •Simple on/off states match electrical circuits
- •Efficient for digital storage and processing
- •Foundation of computer programming
Binary Operations
Addition
Similar to decimal addition, but carry occurs when sum equals 2.
Subtraction
Can use borrowing method or two's complement for negative results.
Multiplication
Similar to long multiplication, but simpler with only 0s and 1s.
Division
Long division process with binary multiplication and subtraction.