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Binary Calculator
About the Binary Calculator
Perform arithmetic and bitwise operations on binary numbers: add, subtract, multiply, divide, AND, OR, XOR, NOT and bit shifts.
How to use the Binary Calculator
- Enter Binary A.
- Choose an Operation.
- Enter Binary B (or the shift amount) and press Calculate.
Formula and method
Binary numbers use only 0 and 1, with each position worth a power of two. Bitwise operations act on each pair of bits independently: AND gives 1 only if both bits are 1, OR gives 1 if either is 1 and XOR gives 1 if the bits differ.
Worked example
1010 + 0110 = 10000 (10 + 6 = 16). 1010 AND 0110 = 0010.
Converting. Binary 1101 = 8 + 4 + 0 + 1 = 13 in decimal, and decimal 45 is 101101 in binary.
When to use the Binary Calculator
- Converting between binary and decimal for computer science classes.
- Doing binary arithmetic and bitwise operations.
- Understanding how computers store numbers.
Common mistakes to avoid
- Reading binary from the wrong end. The rightmost digit is the smallest.
- Forgetting the fixed width when working with signed numbers.
Tips
- Shifting left by one bit doubles a number; shifting right halves it.
- Use the binary calculator with a decimal converter to check your work.
Frequently Asked Questions
Add the powers of two for each position that has a 1. 1010 = 8 + 2 = 10.
Divide by 2 repeatedly and write down the remainders, then read them from bottom to top.
Electronic circuits are simple and reliable with two states, on and off.