Convert binary numbers to decimal and decimal numbers to binary instantly. The tool validates your input, supports very large integers, and shows clear conversion steps.
Choose the conversion direction, enter a whole number, and copy the result. Binary uses only 0 and 1. Decimal uses digits 0–9.
105
The explanation updates as you type. For very large numbers, the tool keeps the result exact and summarizes the method instead of displaying an overly long step list.
BigInt for integer conversion, so large whole numbers are handled exactly instead of being rounded like regular floating-point numbers.
The binary system is base-2. It uses only two digits: 0 and 1.
The decimal system is the everyday base-10 number system. It uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Binary is fundamental in computing because digital circuits represent information with two states, commonly described as off/on or 0/1.
To convert binary to decimal, multiply each binary digit by a power of 2. The rightmost digit uses 20, the next digit uses 21, then 22, and so on.
1101001₂ = 1×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 105₁₀
This means binary 1101001 is equal to decimal 105.
To convert decimal to binary, repeatedly divide the decimal number by 2 and record each remainder. The binary result is the remainders read from bottom to top.
179 ÷ 2 = 89 remainder 1
89 ÷ 2 = 44 remainder 1
44 ÷ 2 = 22 remainder 0
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Result: 10110011₂
So decimal 179 converts to binary 10110011.
This converter focuses on exact whole-number conversion. Binary fractions are possible too: digits after the binary point represent 1/2, 1/4, 1/8, 1/16 and so on.
Binary appears in programming, networking, file formats, bitmasks, permissions, digital electronics and low-level debugging. For readability, long binary values are often grouped or converted to hexadecimal.