Binary Calculator
Perform arithmetic on two binary numbers and convert any value between binary, decimal and hexadecimal.
Example
Add binary 1011 (decimal 11) and 110 (decimal 6):
1011 (11)
+ 110 ( 6)
------
10001 (17) = 0x11
Convert decimal 255: binary 11111111, hex FF.
How it works
Pick an operation and enter two binary numbers to see the result in binary, decimal and hex. Use the converter to translate a single value across all three number bases.
Good to know
This Binary Calculator does two jobs in one screen. The top half performs arithmetic on two binary numbers — addition, subtraction, multiplication, or division — and shows the result simultaneously in binary, decimal, and hexadecimal. The lower half is a standalone base converter that takes a single value entered in binary, decimal, or hex and rewrites it across all three bases. It is aimed at computer-science students, programmers debugging bitwise logic, and anyone studying digital electronics or number systems who wants a quick sanity check without doing the conversions by hand.
Reach for it when you need to verify a calculation rather than learn the long-hand method: confirming the sum of two bit patterns, checking what a hex constant looks like in binary, or working out the integer quotient and remainder of a division. Because everything runs in your browser, it is also handy in exam-prep or offline situations where you do not want to send keystrokes to a server.
Reading the output is straightforward, but a few behaviors are worth knowing. The arithmetic fields accept only the digits 0 and 1; type anything else and the result clears with a prompt to enter valid binary. Division is integer-only, so 1011 divided by 110 gives a whole quotient plus a separate "Remainder (binary)" value, and division by zero is blocked. Subtraction can produce a negative result, which is shown with a leading minus sign on the binary and hex outputs rather than as two's-complement.
- Arithmetic inputs: binary digits only, no minus sign or hex letters.
- Converter input: a leading minus sign is allowed, plus digits valid for the chosen base (A–F for hex).
- All results are whole numbers — there is no fractional or floating-point handling.
Frequently asked questions
What happens when I divide binary numbers?
Division uses integer math: it returns the whole-number quotient in binary plus a separate remainder. For example 1100 (12) ÷ 11 (3) gives quotient 100 (4) with remainder 0, and dividing by zero is blocked.
Can I enter negative or hexadecimal values?
The arithmetic fields accept only binary digits (0 and 1). The converter accepts a leading minus sign and digits valid for the chosen base, including A–F for hexadecimal, and outputs all three bases.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
How do you add two binary numbers by hand?
Line the numbers up by their rightmost bit and add column by column, carrying 1 to the next column whenever a column totals 2 (binary 10) or 3 (binary 11). For example, 1011 + 110 produces carries that yield 10001, which is 17 in decimal.
What is 1011 in decimal?
Binary 1011 equals 11 in decimal. Each bit is a power of two from right to left: 1×8 + 0×4 + 1×2 + 1×1 = 11.
How do you convert binary to hexadecimal?
Group the binary digits into sets of four starting from the right (padding the leftmost group with zeros if needed), then replace each four-bit group with its single hex digit. For instance, 11111111 splits into 1111 1111, which becomes FF.
Why does binary subtraction give a negative result here?
If the second number is larger than the first, ordinary subtraction produces a negative value, and this tool shows it with a leading minus sign rather than using two's-complement notation. The decimal and hex outputs are signed the same way.
Can a binary calculator handle decimal points or fractions?
This one works with whole numbers only, so it does not accept a binary point or produce fractional output. Division returns an integer quotient and a separate remainder instead of a decimal fraction.
What is the difference between binary, decimal, and hexadecimal?
They are number systems with different bases: binary is base-2 (digits 0–1), decimal is base-10 (digits 0–9), and hexadecimal is base-16 (digits 0–9 then A–F). They represent the same quantities in different notations, which is why one value can be shown in all three.
Why do computers use binary instead of decimal?
Digital hardware stores and switches information using two stable states, typically on and off or high and low voltage, which map naturally to the two digits of binary. This makes binary the simplest and most reliable way to represent data inside electronic circuits.
What does the remainder mean in binary division?
Because the calculator uses integer division, the remainder is whatever is left over after dividing as many whole times as possible. For example, dividing 12 (1100) by 3 (11) gives quotient 4 (100) with remainder 0, while a non-even division would show a non-zero remainder in binary.
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