Binary Calculator
Use this free Binary Calculator to calculate your Binary arithmetic instantly and accurately.
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Result
What is a Binary Calculator?
A Binary Calculator converts numbers between binary (base 2), decimal (base 10), hexadecimal (base 16), and octal (base 8). It handles base conversions and binary arithmetic operations.
How to convert decimal to binary manually (the formula)
Repeatedly divide the decimal number by 2. Record the remainder (0 or 1) at each step. Read the remainders from the last division to the first to get the binary equivalent.
Example calculation
Convert 13 to binary. 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading remainders from bottom to top: 1101. So 13 in binary is 1101.
Common mistakes
- Reading remainders in the wrong order — The last remainder is the most significant bit (leftmost), not the first.
- Using incorrect base symbols — Binary uses only 0 and 1. Digits 2–9 are invalid in binary.
- Confusing binary and decimal in addition — In binary, 1 + 1 = 10 (not 2). Carry the 1 to the next column.
Frequently asked questions
What is binary?
Binary is a base-2 number system that uses only two digits: 0 and 1.
How do I convert decimal to binary?
Repeatedly divide by 2 and read the remainders from bottom to top.
How do I add binary numbers?
Add bit by bit using: 0+0=0, 0+1=1, 1+0=1, 1+1=0 carry 1.
What is the binary representation of 42?
42 in binary is 101010.
Why do computers use binary?
Computers use binary because transistors have two stable states (on/off).