Binary Calculator
Add, subtract, multiply, and divide binary numbers online free. Shows step-by-step working and decimal equivalents for every operation. No signup needed.
How to Use Binary Calculator
- 1Enter your first binary number using only 0s and 1s.
- 2Select the operation: addition (+), subtraction (−), multiplication (×), division (÷), or bitwise (AND, OR, XOR).
- 3Enter your second binary number.
- 4Click Calculate to see the binary result with step-by-step working.
- 5Review the decimal equivalents shown for all values to verify the conversion.
About Binary Calculator
This binary calculator online free performs arithmetic directly on binary numbers — addition, subtraction, multiplication, and division — with full step-by-step working shown for every calculation. It also supports bitwise operations including AND, OR, XOR, NOT, and left/right shifts.
Want to add binary numbers online for a homework problem? Need to check binary multiplication step by step for a digital electronics exam? Enter your operands in binary (0s and 1s only), select the operation, and the full working appears alongside the binary result and its decimal equivalent.
Binary division with remainder is shown clearly so you can follow the long-division algorithm used in digital arithmetic. This makes the calculator useful not just for getting answers but for understanding how binary arithmetic actually works inside a CPU.
The binary AND OR calculator functionality makes it useful for low-level programming, bitmask operations, and Boolean logic problems. All results include the decimal equivalents so you can immediately verify the conversion.
How Binary Calculator Works
The Binary Calculator performs arithmetic operations — addition, subtraction, multiplication, and division — directly on binary (base-2) numbers. It also supports bitwise operations: AND, OR, XOR, NOT, left shift (<<), and right shift (>>). Input two binary numbers using only 0s and 1s. The calculator shows the binary result alongside its decimal and hexadecimal equivalents. For arithmetic, it uses standard two's complement representation for handling negative numbers in subtraction. For bitwise operations, it performs the logic gate operation on each corresponding pair of bits, making the result easy to trace step by step.
Binary Addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1)
AND: 1 only if both bits are 1
OR: 1 if either bit is 1
XOR: 1 if bits differ
Left shift (n<<k): multiply by 2^k
Right shift (n>>k): divide by 2^k (integer)Who Uses This Tool and Why
- ✓Computer science students practice binary arithmetic and bitwise logic for coursework, verifying hand-calculated results for binary addition, subtraction, and XOR operations.
- ✓Embedded systems and firmware developers calculate bitmask values for hardware register configuration, using AND and OR operations to set and clear specific control bits.
- ✓Networking professionals verify subnet masks and perform binary AND operations between IP addresses and subnet masks to calculate the network address.
- ✓Security researchers use XOR operations to trace simple encryption algorithms and understand how XOR-based ciphers work at the bit level.
- ✓Developers implementing low-level optimisations use the shift calculator to verify that left-shift (×2ⁿ) and right-shift (÷2ⁿ) produce the expected results for power-of-two multiplications.
Limitations & Practical Tips
Known Limitations
- •The tool works with unsigned integers up to 32 bits by default. Signed two's complement arithmetic for negative numbers in subtraction follows standard 8/16/32-bit overflow rules.
- •Division of binary numbers may produce non-integer results; the calculator shows the integer quotient and remainder (not a fractional binary result).
- •Very large binary numbers (more than 32 bits) may produce results beyond JavaScript's safe integer range — use a BigInt-aware tool for precision at that scale.
Tips for Best Results
- →For bitmask operations, remember: AND clears bits (use to mask off), OR sets bits (use to add flags), XOR toggles bits (use to flip). This is the core of all flag register manipulation.
- →Left-shifting n by k positions is equivalent to multiplying n by 2^k — this is a common micro-optimisation in performance-critical code.
- →When adding two binary numbers, work from right to left just as in decimal addition, carrying 1s to the next column whenever you get a sum of 2 (10 in binary).
Frequently Asked Questions
- How does binary addition work?
Binary addition follows the same column-by-column process as decimal addition, but with only two digits (0 and 1). Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1). Example: 1010 + 0110 = 10000 (10 + 6 = 16 in decimal).
- How does binary subtraction work?
Binary subtraction follows the same borrow rules as decimal. When borrowing, 1 ten (1 in decimal) becomes 10 binary (2 in decimal), so 10 − 1 = 1. Example: 1010 − 0110 = 0100 (10 − 6 = 4 in decimal). The calculator handles the borrowing automatically.
- What is a bitwise AND operation?
Bitwise AND compares each bit position: the result bit is 1 only if both input bits are 1. Example: 1010 AND 1100 = 1000 (bits aligned: only position 3 has both bits as 1). AND is used for masking — isolating specific bits by ANDing with a mask.
- What is XOR used for in computing?
XOR (exclusive OR) produces 1 when bits differ, 0 when they are the same. It is used in: cryptography (simple XOR cipher, hash functions), parity checks, swap algorithms (XOR swap without a temp variable), RAID storage parity, and generating checksums. XOR-ing a value with itself always gives 0.
- What does left shift (<<) do?
Left shift moves all bits left by the specified number of positions, filling from the right with zeros. Each left shift by 1 doubles the value (equivalent to multiplying by 2). Example: 0011 << 2 = 1100 (3 << 2 = 12 = 3 × 4). Right shift (>>) divides by powers of 2.
- How do I enter a negative binary number?
Enter the magnitude as a positive binary number — the subtraction operation handles negativity. For example, to compute −5 + 3, calculate 5 − 3 = 2 separately. Two's complement representation of negative numbers is used internally but the display shows decimal for negative results.
- What is the maximum binary number I can calculate with?
The calculator uses JavaScript's standard 32-bit integer for bitwise operations (AND, OR, XOR, shifts) and 53-bit safe integers for arithmetic. For bitwise operations, inputs are coerced to 32-bit signed integers, so very large binary numbers may have unexpected results — use arithmetic mode for large values.
Looking for more tools like this? Browse all Calculator Tools →
More Calculator Tools
Percentage Calculator
Calculate percentages, percentage change, and what percent one number is of another. Free online percentage calculator for everyday math.
Age Calculator
Calculate exact age in years, months, and days from a birth date. Free online age calculator with next birthday countdown and life statistics.
TDEE Calculator
Calculate your Total Daily Energy Expenditure free online. Find your daily calorie needs based on weight, height, age, and activity level instantly.
BMI Calculator
Calculate your Body Mass Index free online. Enter your height and weight to get your BMI score, category, and healthy weight range instantly.
Tip Calculator
Calculate tips and split bills free online. Enter your bill total, tip percentage, and number of people to instantly see tip amount and per-person cost.
Compound Interest Calculator
Calculate compound interest growth on savings and investments free online. See how money grows over time with annual, monthly, or daily compounding.
You Might Also Like
Word Counter
Count words, characters, sentences, and paragraphs instantly. Free online word counter tool with reading time estimate for writers and students.
Character Counter
Count characters with and without spaces instantly. Free online character counter for Twitter, Instagram, SMS, and meta tag length limits.
JSON Formatter
Format, validate, and minify JSON online. Instantly beautify or compress JSON data with syntax highlighting. Free JSON formatter and validator.
Last updated: May 2, 2026 — Binary Calculator by CalcDash.