Perform arithmetic operations on binary numbers with step-by-step breakdowns.
2026-03-28T00:00:00Z
Binary is a base-2 number system that uses only two digits: 0 and 1. Unlike our everyday decimal system (base-10) which uses ten digits (0-9), binary represents all numbers using combinations of zeros and ones. Each position in a binary number represents a power of 2, just as each position in decimal represents a power of 10.
Binary arithmetic follows the same fundamental rules as decimal arithmetic, but with simpler addition and multiplication tables since we only have two digits. In binary addition: 0+0=0, 0+1=1, 1+0=1, and 1+1=10 (where the 1 carries to the next position). This simplicity makes binary ideal for digital computers, which use electrical signals (on/off, high/low voltage) to represent data.
Understanding binary arithmetic is fundamental to computer science, digital electronics, and programming. Every piece of data in a computer—numbers, text, images, videos—is ultimately stored and processed as binary. Binary operations are used in networking (IP addresses), cryptography, data compression, graphics programming, and low-level system operations. Mastering binary arithmetic helps you understand how computers work at the most fundamental level.
Limitations: This calculator works with positive integers and integer division only. Negative results are shown with a minus sign (not true two's complement). For production cryptography or low-level system work, use proper signed integer representations.
Enter your first binary number using only 0s and 1s (e.g., 1010, 1111, 101). The calculator will automatically display the decimal equivalent below each input to help you verify your numbers.
Select the arithmetic operation you want to perform: addition (+), subtraction (-), multiplication (×), or division (÷). The selected operation will be highlighted in cyan.
The result appears instantly in both binary and decimal formats. The calculator also shows the complete equation with both number systems for easy verification and learning.
Save calculations to history for reference, or use the Reset button to clear all fields and start a new calculation. History keeps your last 5 binary operations.
A network administrator needs to calculate the number of available IP addresses by performing binary operations on subnet masks.
This binary calculation is essential for network engineers when designing IP address schemes, calculating subnet sizes, and optimizing network architecture.
Add column by column from right to left, just like decimal. Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1). Example: 101 + 011 = 1000.
Binary is base-2 (uses 0,1), decimal is base-10 (uses 0-9). Binary positions represent powers of 2 (1,2,4,8...), while decimal represents powers of 10 (1,10,100,1000...).
Similar to decimal multiplication: multiply each digit, shift left for each position, then add results. Since digits are only 0 or 1, you either write the number (×1) or write zeros (×0).
Yes! Computers use two's complement representation for negative numbers. The leftmost bit indicates sign (0=positive, 1=negative), enabling arithmetic with both positive and negative values.
Digital circuits work with two states: on/off, high/low voltage. Binary maps perfectly to these states, making it reliable and simple to implement in hardware. It's the foundation of all digital computing.
Repeatedly divide by 2, keeping track of remainders. Read remainders bottom-to-top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 1101.
Similar to long division in decimal, but simpler. Determine how many times the divisor fits into portions of the dividend, subtract, and bring down the next digit. Result uses only 0s and 1s.
Everywhere in technology: computer processors, memory, networking (IP addresses), file systems, cryptography, digital communications, image/video encoding, and all digital data storage and transmission.
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