Binary calculator
Run arithmetic across binary, octal, decimal, or hex operands and view the result in all four bases.
What this calculator covers
Use this calculator when you want base arithmetic without manually translating every operand by hand.
The result table makes it easy to compare the same value in binary, octal, decimal, and hexadecimal after one addition, subtraction, multiplication, or division step.
Frequently asked questions
- Can I enter a decimal number and see it converted to binary?
- Yes. Set both the operand base and operator to produce the value you want, or enter the decimal number with a second operand of zero and use addition. The result table always shows the answer in all four bases simultaneously.
- What bases does this calculator support?
- You can enter operands in binary (base 2), octal (base 8), decimal (base 10), or hexadecimal (base 16). The arithmetic is performed once in decimal internally, and the result is expressed in all four bases.
- How does division work across number bases?
- Division operates on the decimal equivalents of your operands and produces an exact decimal result. That result is then converted back into each base for display, so fractional remainders appear in decimal form rather than as binary fractions.
- Why would I use octal instead of hexadecimal?
- Octal is less common today but still appears in Unix file permission notation and some legacy systems. Hexadecimal is more widely used for memory addresses and color codes. This calculator supports both so you can work in whichever base your context requires.
Tool
Run the calculation
Result
RESULT · BASE ARITHMETIC
â„–149
Primary result
10001 (base 2) = 17 (base 10)
1011 + 110 in binary equals 10001 in the selected base and 17 in base 10.
- Selected-base result
- 10001 (base 2)
- Binary
- 10001
- Octal
- 21
- Decimal
- 17
- Hex
- 11
Step-by-step solution
- 1.Interpret 1011 and 110 as binary integers, which correspond to 11 and 6 in base 10.
- 2.Apply addition in base 10 to get 17.
- 3.Rewrite that same value across the base table so the selected-base result is 10001, with binary 10001, octal 21, decimal 17, and hex 11.
Walkthrough
Visual walkthrough
Base arithmetic becomes transparent when the operands are decoded once, solved once, and then re-encoded into each requested base.
01
Decode the operands
1011 -> 11, 110 -> 6
Each operand is interpreted using the selected radix before any arithmetic is applied.
02
Run the arithmetic once
11 + 6 = 17
The underlying value is the same no matter how the digits are written.
03
Render the result in each base
bin 10001 | oct 21 | dec 17 | hex 11
Once the value is known, each numeral system is just a different surface encoding of the same quantity.
10001 in binary