Binary Calculator

Division performs standard integer division, throwing away remainder fractions (floor division).

Negative results are prefixed with a standard minus sign in our viewer for easy conceptual reading.

A binary calculator performs arithmetic operations (addition, subtraction, multiplication, division) and bitwise logic gates (AND, OR, XOR) on binary numbers.

The binary number system uses only two digits: 0 and 1. It is the fundamental language of computers and digital electronics.

Binary addition follows the same rules as decimal addition but with only two digits: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry).

Binary subtraction follows the same rules as decimal subtraction: 0-0=0, 1-0=1, 1-1=0, 0-1=1 (borrow).

Binary multiplication is simpler than decimal: 0×0=0, 0×1=0, 1×0=0, 1×1=1. Shift and add like decimal multiplication.

Binary division follows the same long division process as decimal, using only 0s and 1s.

Bitwise AND compares each bit position: output is 1 only if both corresponding bits are 1.

Bitwise OR compares each bit position: output is 1 if at least one corresponding bit is 1.

Bitwise XOR compares each bit position: output is 1 if the corresponding bits are different.

A bit is the smallest unit of data in computing, representing either a 0 or a 1.

A byte consists of 8 bits. It can represent values from 0 to 255 in decimal.

Each binary digit represents a power of 2. Sum the powers of 2 for each 1-bit position to convert to decimal.

Repeatedly divide by 2 and record remainders. Read remainders from bottom to top for the binary representation.

Two's complement is a method of representing negative binary numbers. Invert all bits and add 1.

Binary overflow occurs when the result of an operation exceeds the maximum value that can be stored in the available bits.

A carry occurs in addition when the sum of two bits exceeds 1, requiring a carry to the next higher bit position.

A borrow occurs in subtraction when subtracting 1 from 0, requiring a borrow from the next higher bit position.

Enter two binary numbers. The calculator adds them bit by bit from right to left, handling carries.

Enter two binary numbers. The calculator subtracts the second from the first, handling borrows.

Enter two binary numbers. The calculator multiplies using shift-and-add method.

Enter two binary numbers. The calculator performs long division in binary.

Enter two binary numbers. The calculator performs bitwise AND on each bit position.

Enter two binary numbers. The calculator performs bitwise OR on each bit position.

Enter two binary numbers. The calculator performs bitwise XOR on each bit position.

Enter a binary number. The calculator converts it to its decimal equivalent.

Enter a decimal number. The calculator converts it to its binary representation.

Enter a binary number. The calculator converts it to hexadecimal (base-16).

Enter a binary number. The calculator converts it to octal (base-8).

Enter two binary numbers, select an operation (add, subtract, multiply, divide, AND, OR, XOR), and click "Calculate".

Enter sequences of 0s and 1s. The calculator validates that only binary digits are used.

The calculator automatically pads shorter numbers with leading zeros to match bit lengths.

Binary is the fundamental language of computers. All digital data is ultimately represented in binary.

Bitwise operations are used in programming, cryptography, networking, and digital logic design.

Understanding binary arithmetic helps with computer science, programming, and digital electronics.

Binary is used because electronic circuits have two states (on/off), naturally representing 0 and 1.

Different number systems are used in different contexts: binary for computers, hex for memory addresses, decimal for human use.

Binary addition is the foundation of all computer arithmetic operations.

Bitwise operations are performed directly on individual bits, making them extremely fast in hardware.

Yes. The calculator pads shorter numbers with leading zeros to match lengths.

Yes. Enter two binary numbers for subtraction with automatic borrow handling.

Yes. Enter two binary numbers for multiplication using shift-and-add.

Yes. Enter two binary numbers for integer division with remainder.

Yes. Perform AND, OR, and XOR on any two binary numbers.

Yes. Convert between binary, decimal, hexadecimal, and octal.

Yes. The calculator supports binary numbers of any length.

Yes. The calculator helps verify bitwise operations and binary arithmetic for programming.

Yes. The calculator is useful for computer science and digital logic homework.

Yes. The calculator performs precise binary arithmetic and logic operations.

Yes. The binary calculator is completely free with no registration.

Yes. All calculations are performed in your browser with no data transmitted.

Yes. The calculator implements standard binary arithmetic and logic operations.

Yes. Students use this calculator for computer science and digital logic courses.

Yes. The calculator is regularly updated to ensure accuracy.

Yes. The calculator works on smartphones, tablets, and desktop computers.

Yes. The calculator eliminates errors in binary arithmetic and logic operations.

Yes. Programmers use binary calculations for bitwise operations and data manipulation.

Yes. Engineers use binary arithmetic for digital logic and circuit design.

Binary uses base-2 (0,1). Decimal uses base-10 (0-9). Binary is used in computers; decimal is used by humans.

AND outputs 1 only if both bits are 1. OR outputs 1 if at least one bit is 1.

OR outputs 1 if any bit is 1. XOR outputs 1 only if bits are different.

Binary is base-2. Hexadecimal is base-16, used as a compact representation of binary data.

Binary is base-2. Octal is base-8, used in some programming contexts.

Unsigned represents only positive numbers. Signed uses two's complement for negative numbers.

Binary addition has only two digits and carries at 2. Decimal addition has ten digits and carries at 10.

A bit is a single binary digit (0 or 1). A byte is 8 bits.

Shift moves bits left/right, filling with zeros. Rotate wraps bits around.

Binary calculator performs operations. Logic simulator visualizes digital circuits.

When working with computer data, digital electronics, or low-level programming.

In programming (flags, masks), cryptography, networking (IP addresses), and hardware design.

When debugging code, reading memory dumps, or working with different data representations.

IP addresses, subnet masks, and network configurations use binary representation.

When performing bitwise operations, bit manipulation, or working with binary data.

The Binary Calculator uses standard mathematical formulas validated against authoritative references. The specific formula is displayed in the calculator interface with a detailed explanation of each variable.

Each calculator includes a step-by-step worked example showing exactly how the formula is applied. You can follow these steps with pen and paper to verify any result.

The Binary Calculator accepts numeric inputs including integers and decimals. Invalid inputs (letters, special characters) are rejected with clear error messages.