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Write down any logical number (binary, octal, decimal, or hexadecimal), and the binary calculator will assist you in applying arithmetic operations to them.
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This online binary calculator allows you to perform arithmetic operations on two binary numbers, as well as on octal, decimal, and hexadecimal numbers. It provides exact results and step-by-step calculations for addition, subtraction, multiplication, and division.
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system, using only two symbols: 0 (zero) and 1 (one). Each digit is called a bit, short for binary digit. Binary numbers are positional, meaning the position of each digit determines its value.
Example: The binary number 101 is pronounced as “one zero one” or “one-oh-one.” The number 111010 consists of six bits.
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 7 | 111 |
| 8 | 1000 |
| 10 | 1010 |
| 16 | 10000 |
| 20 | 10100 |
You can also convert decimal numbers to fractions using a decimal to fraction calculator or convert fractions to decimals using a fraction to decimal calculator.
The binary calculator performs arithmetic operations on numbers in the same base:
Binary addition is similar to decimal addition but carries over 1 instead of 10.
| A + B | Sum | Carry |
|---|---|---|
| 0 + 0 | 0 | 0 |
| 0 + 1 | 1 | 0 |
| 1 + 0 | 1 | 0 |
| 1 + 1 | 0 | 1 |
Example: Add (10110010)2 and (11101)2
10110010 + 11101 ------------- 11001111
Binary subtraction is like decimal subtraction but borrows 1 instead of 10.
Example: Subtract (11101)2 from (100011)2
100011
- 11101
-------------
000110
Binary multiplication uses only 0 and 1. It is simpler than decimal multiplication.
Example: Multiply (101011)2 by (101)2
101011
x 101
----------------
101011
000000
+ 101011
----------------
11010111
Binary division is similar to long division in decimal.
Example: Divide (101010)2 by (110)2
111
------
110 |101010
110
------
1010
110
------
100
The calculator displays results in all four number systems: binary, decimal, octal, and hexadecimal.
99 is a decimal number. Binary numbers contain only 0 and 1.
A binary number is a number expressed in base 2, using only 0 and 1.
Binary numbers are used in computers, logic gates, and electronic devices. They are the basis of Boolean algebra and digital electronics.
Binary numbers simplify computing and electronic design. This online binary calculator allows you to perform arithmetic operations easily and accurately.
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