Binary / Octal / Hex Arithmetic Calculator — Add, Subtract & Multiply
Add, subtract or multiply two numbers entered directly in binary, octal or hexadecimal — see the answer in the working base and in decimal, with a column-by-column "show work" view of every carry and borrow. Runs entirely in your browser.
How to Use
- Pick the base you are working in — binary (base 2), octal (base 8) or hexadecimal (base 16).
- Type your two numbers in that base (only valid digits are accepted — e.g. 0 and 1 for binary).
- Choose the operation: add (+), subtract (−) or multiply (×).
- Read the result in the working base and in decimal — the answer updates live as you type.
- Open the column-by-column working to follow every carry, borrow and partial product by hand.
Do the maths in the base you actually work in
Most calculators force you to convert binary or hexadecimal to decimal, do the sum, and convert back. This one keeps you in the working base the whole time. Type both operands in binary (base 2), octal (base 8) or hexadecimal (base 16), pick add, subtract or multiply, and read the answer straight back in that base — with the decimal value alongside as a sanity check. Internally every operand is parsed to an exact integer (using BigInt, so even very long hex strings stay correct), the operation is computed, and the result is formatted back into your base. The “Show work” panel then redoes the operation in the base, column by column, so you can see precisely where each carry and borrow lands.
Carries, borrows and partial products
Addition works right-to-left just like decimal, except a column “rolls over” when its total reaches the base. In binary 1 + 1 = 10₂, so the column writes 0 and carries 1; in hex a column carries once its total reaches 16. That is why FF + 1 = 100₁₆ (decimal 256) — both columns carry. Subtraction borrows from the next column when the top digit is too small; a borrow is worth the whole base (16 in hex, 8 in octal, 2 in binary), so 1010 − 11 = 111₂ (decimal 7). Multiplication is shown as partial products — multiply by each digit of the second number, shift left by that digit’s position, and add the rows. The carry row is drawn above the digits so the method matches what you would write on paper.
Quick reference
About the Binary / Octal / Hex Arithmetic Calculator — Add, Subtract & Multiply
Use the Binary / Octal / Hex Arithmetic Calculator — Add, Subtract & Multiply — a free, easy tool for everyday tasks. Nothing is uploaded, and you do not need an account. Add, subtract or multiply two numbers entered directly in binary, octal or hexadecimal — see the answer in the working base and in decimal, with a column-by-column "show work" view of every carry and borrow. Runs entirely in your browser.
How it works
Put each value in its box and read the answer as you go. Because it recalculates live, you can play with the inputs to see how each one moves the result — handy for checking your own working or planning ahead. Everything happens on your device, so it is fast and private.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
How does binary addition with carries work?
You add column by column from the right, exactly like decimal, but you carry whenever a column total reaches the base. In binary, 1 + 1 = 10, so the column shows 0 and you carry 1 into the next column. For example 1010 + 110: the columns give 0, 1, carry into the third column, then 1 — producing 10000 (decimal 16). The "show work" panel prints the carry above each column.
How do borrows work when subtracting in hex or octal?
When the top digit in a column is smaller than the bottom digit you borrow 1 from the next column to the left, which is worth the base (16 in hex, 8 in octal, 2 in binary). So in hex a borrow adds 16 to the current column. The working view marks each borrowed column so you can see where the deficit came from.
Can the result be negative?
Yes. Subtraction can give a negative answer (the calculator shows a leading minus sign in both the working base and decimal). Addition and multiplication of the values you type are always non-negative here, since the inputs are unsigned magnitudes.
Why convert to decimal at all?
The decimal value is the universal sanity check — FF + 1 in hex is 100, which is 256 in decimal, and 7 + 1 in octal is 10, which is 8. Seeing both side by side makes it obvious when a carry has rolled the number into a new column.
Is anything uploaded?
No. Every digit is parsed and the arithmetic is done in your browser with JavaScript (using BigInt for exact results on large values). Nothing is sent to a server.
How do I use the Binary / Octal / Hex Arithmetic Calculator — Add, Subtract & Multiply?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Learning number systems
Practise binary, octal and hex addition, subtraction and multiplication with every carry and borrow spelled out, then check the decimal answer.
Low-level programming
Add an offset to a hex memory address, combine bitmask values, or work out the size of a region without dropping back to decimal.
Digital logic & CS courses
Verify homework on base-2 arithmetic, two’s-complement reasoning and carry propagation against a worked example.
Unix permissions & flags
Combine or adjust octal permission bits and see the binary and decimal equivalents at the same time.
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