Binary Calculator & Number Base Converter
Convert between binary, quinary, octal, decimal, and hexadecimal — and calculate in any base. Type in any box. Everything updates live. No buttons, no sign-up.
Converter
All five boxes are editable. Type in any one and the other four convert in real time.
Calculator
Pick a base, type two numbers in that base, pick an operation. The result updates live — including quotient and remainder for division.
How to convert decimal to binary
- Divide by 2. Divide the decimal number by 2 and write down the remainder.
- Repeat with the quotient. Divide the quotient by 2 again and write down the remainder. Keep going until the quotient is 0.
- Read the remainders bottom to top. The binary number is the remainders read from the last division up to the first.
- Check with RadixFlip. Type the decimal number into the Decimal box and compare the Binary box.
Example: 42 → 101010. Try it: type 42 in the Decimal box and watch all five boxes fill in.
Frequently asked questions
What is a binary calculator?
A binary calculator is a tool that works with base-2 numbers — numbers made only of 0s and 1s. RadixFlip converts between binary, quinary, octal, decimal, and hexadecimal, and adds, subtracts, multiplies, and divides numbers in any of those bases.
How do I convert decimal to binary?
Divide the decimal number by 2, write down the remainder, and repeat with the quotient until the quotient is 0. Then read the remainders bottom to top. For example, 42 ÷ 2 = 21 remainder 0, 21 ÷ 2 = 10 remainder 1, 10 ÷ 2 = 5 remainder 0, 5 ÷ 2 = 2 remainder 1, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1 — reading the remainders bottom to top gives 101010. Type 42 in the Decimal box above and RadixFlip shows every step of the result instantly.
How do I add binary numbers?
Add binary numbers column by column from right to left, just like decimal, but carry 1 whenever a column sums to 2 or more: 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 0 carry 1, and 1 + 1 + 1 (with a carry) = 1 carry 1. For example, 1010 + 1011 = 10101. Switch to the Calculator section above, pick Binary, and try it live.
How do I use binary on a Casio calculator?
On most Casio scientific calculators, press MODE until you see BASE-N, then select it. You can then switch between DEC, HEX, BIN, and OCT with the dedicated keys and type numbers in the selected base. RadixFlip covers the same conversions plus quinary, and shows every base at once so you can check your Casio result.
What is radix?
Radix is the technical word for the base of a number system — how many distinct digits it uses. Binary has radix 2, quinary radix 5, octal radix 8, decimal radix 10, and hexadecimal radix 16. That is why this site is called RadixFlip: it flips numbers between radices.
How do I convert hexadecimal to binary?
Convert each hexadecimal digit to its 4-bit binary group, then join the groups: 0 = 0000, 1 = 0001, 2 = 0010, 3 = 0011, 4 = 0100, 5 = 0101, 6 = 0110, 7 = 0111, 8 = 1000, 9 = 1001, A = 1010, B = 1011, C = 1100, D = 1101, E = 1110, F = 1111. For example, 2A becomes 0010 1010, which is 101010. Type any hex value in the Hexadecimal box above to see it converted.
Why convert between number bases?
Computers store everything as binary. Programmers use hexadecimal as a compact shorthand for binary, and octal shows up in file permissions and older systems. Decimal is the everyday base, and quinary (base 5) is a useful teaching base because it is small enough to work through by hand. Flipping between them is a core skill in computer science classes — and this page is built to make it instant to check your work.