Binary Calculation

Enter two binary numbers, pick an operation, read the result. Everything updates live as you type.

Binary Calculator

Enter first number =

Enter second number =

Result = 10101 in binary (21 in decimal).

Full calculator (all five bases) → · Binary addition calculator →

How to calculate binary numbers

Enter the first number. Use only 0s and 1s.
Pick an operation. + add, − subtract, × multiply, ÷ divide (quotient + remainder).
Enter the second number. The result updates live below the line.
Check the other bases. The result is also shown in quinary, octal, decimal, and hex.

Worked examples

Calculation	Binary result	Decimal check
1010 + 1011	10101	10 + 11 = 21
1011 − 1010	1	11 − 10 = 1
101 × 11	1111	5 × 3 = 15
1010 ÷ 10	101 remainder 0	10 ÷ 2 = 5

Rules to remember: 1 + 1 = 0 carry 1. 10 − 1 = 1 (borrow). 1 × 1 = 1, anything × 0 = 0. Dividing by zero is not allowed.

How to calculate binary numbers in code

Python

def binary_calc(a, b, op):
    x, y = int(a, 2), int(b, 2)
    if op == "+": result = x + y
    elif op == "-": result = x - y
    elif op == "*": result = x * y
    elif op == "/": result = x // y  # quotient; remainder is x % y
    return bin(result)[2:] if result >= 0 else "-" + bin(-result)[2:]

print(binary_calc("1010", "1011", "+"))  # 10101

Java

// Add two binary strings
String sum = Integer.toBinaryString(
    Integer.parseInt("1010", 2) + Integer.parseInt("1011", 2)
); // "10101"
// Subtract / multiply: same pattern with - and *.
// Divide: quotient = a / b, remainder = a % b after parsing.

C

#include <stdio.h>
#include <string.h>

int binaryToInt(const char *bits) {
    int result = 0;
    for (size_t i = 0; i < strlen(bits); i++)
        result = result * 2 + (bits[i] - '0');
    return result;
}

void printBinary(int n) {
    if (n == 0) { printf("0"); return; }
    if (n < 0) { putchar('-'); n = -n; }
    char bits[64]; int i = 0;
    while (n > 0) { bits[i++] = (n % 2) + '0'; n /= 2; }
    for (int j = i - 1; j >= 0; j--) putchar(bits[j]);
}

int main(void) {
    int sum = binaryToInt("1010") + binaryToInt("1011");
    printBinary(sum); // prints 10101
    return 0;
}

These snippets assume valid binary input (only 0s and 1s). RadixFlip validates the input for you.

Frequently asked questions

How do I calculate binary numbers?

Enter the first binary number, pick an operation (+, −, ×, ÷), enter the second binary number, and read the result. Binary addition: 1 + 1 = 0 carry 1. Subtraction borrows 1 (10 − 1 = 1). Multiplication: shift and add. Division: quotient + remainder. Type two numbers in the calculator above and the result updates live.

What is 1010 + 1011 in binary?

1010 + 1011 = 10101 in binary, which is 21 in decimal. Check: 1010 is 10, 1011 is 11, and 10 + 11 = 21.

How do I subtract binary numbers?

Subtract column by column from right to left, borrowing 1 when needed: 0 − 1 needs a borrow (10 − 1 = 1). Example: 1011 − 1010 = 1 in binary (11 − 10 = 1 in decimal). The calculator above handles borrows for you.

How do I multiply binary numbers?

Multiply like decimal, but every partial product is 0 or the other number: 1 × 1 = 1, anything × 0 = 0. Example: 101 × 11 = 1111 in binary (5 × 3 = 15 in decimal). Shift the second number left for each 1-bit and add.

How do I divide binary numbers?

Divide like decimal long division: find how many times the divisor fits, subtract, bring down the next bit, repeat. The answer is a quotient plus a remainder. Example: 1010 ÷ 10 = 101 remainder 0 in binary (10 ÷ 2 = 5 in decimal). Dividing by zero is not allowed.

How do I calculate binary numbers in Python?

Convert with int(x, 2), do the operation in decimal, then convert back with bin(result)[2:]. Example: bin(int("1010", 2) + int("1011", 2))[2:] gives "10101".

Binary addition calculator → · How to convert binary to decimal →