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Binary Calculator
Binary arithmetic, bitwise operations and two's complement.
Binary arithmetic
—
Bitwise operations
—
Two's complement
How computers store negative integers: invert every bit, then add one.
Quick Tool Overview
The Binary Calculator does arithmetic directly in binary — addition, subtraction, multiplication and division — with the decimal equivalent beside every operand and result. A bitwise panel covers AND, OR, XOR, NOT and shifts, and two's complement is handled explicitly.
- What it does
- Performs binary arithmetic and bitwise operations
- You give it
- Binary numbers and an operation
- You get back
- The binary result with its decimal value and bit pattern
- Best for
- Computer science study, embedded work and bit manipulation
About the Binary Calculator
Do arithmetic directly in binary — addition, subtraction, multiplication and division — with the decimal equivalent shown alongside every operand and result so you can check the work.
A bitwise panel covers the operations that matter in programming: AND, OR, XOR, NOT and left and right shifts, with the bit pattern displayed for both inputs and the output. Two's complement is handled explicitly, which is how computers actually represent negative integers: invert every bit and add one. Seeing the bits line up makes it obvious why shifting left doubles a number and shifting right halves it.
Key features of the Binary Calculator
Arithmetic in binary
Add, subtract, multiply and divide without converting to decimal and back first.
Decimal shown throughout
Every operand and result carries its decimal equivalent so you can check the work.
Full bitwise set
AND, OR, XOR, NOT and left and right shifts, with the bit pattern displayed for both inputs and the output.
Two's complement made explicit
Invert every bit and add one — how computers actually represent negative integers, shown step by step.
Shifts made obvious
Seeing the bits line up makes it clear why shifting left doubles a number and shifting right halves it.
How to use the Binary Calculator
-
1
Enter binary numbers
Type using only 0 and 1. The decimal equivalent is shown as you type so you can confirm the value.
-
2
Choose an operation
Pick an arithmetic operation, or switch to the bitwise panel for AND, OR, XOR, NOT and shifts.
-
3
Read the bit pattern
Results are shown in binary, decimal and hexadecimal, with the bits aligned for comparison.
Frequently asked questions
Column by column, carrying when the sum reaches two. 1 plus 1 is 0 carry 1, so binary 1011 plus 1101 gives 11000, which is 11 plus 13 equals 24 in decimal.
The standard way computers store negative integers. Invert all the bits of the positive value and add one. It means addition and subtraction use the same circuitry, with no separate sign bit handling.
OR gives 1 when either bit is 1, including when both are. XOR gives 1 only when exactly one bit is 1, so it returns 0 when both are 1.
Shifting left by one doubles the value, shifting right by one halves it and discards the remainder. It is a fast alternative to multiplying or dividing by powers of two.
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