What is binary arithmetic?

Binary arithmetic is the system of performing mathematical operations (addition, subtraction, multiplication, division) using only the digits 0 and 1, which is the native number system of computers and digital electronics.

How do you add binary numbers?

Binary addition follows the same column-by-column rules as decimal addition but with base-2 carries. 0+0=0, 0+1=1, 1+1=10 (write 0 carry 1), 1+1+1=11 (write 1 carry 1). This calculator shows the carry row step-by-step.

What are bitwise operators?

Bitwise operators act on individual bits of integers. AND returns 1 only when both bits are 1. OR returns 1 when at least one bit is 1. XOR returns 1 when bits differ. NOT flips every bit. Left/right shifts move all bits by a given number of positions.

How is binary different from hexadecimal?

Binary (base 2) uses only 0 and 1, producing long strings. Hexadecimal (base 16) uses 0-9 and A-F; each hex digit represents exactly 4 binary bits (a nibble), making it a compact notation for binary data.

What is a bitwise AND used for?

Bitwise AND is commonly used to mask bits — isolating specific bits in a value by ANDing with a mask where only those bit positions are 1. It is used in permissions checks, network subnetting, and low-level hardware programming.

How do I convert binary to ASCII text?

Split the binary string into 8-bit (or 7-bit) groups. Convert each group from binary to its decimal value, then look up the corresponding ASCII character. For example, 01001000 = 72 = "H".

What is the maximum number this calculator supports?

The arithmetic and bitwise sections support values up to 32 bits (0 to 4,294,967,295 for unsigned). Inputs exceeding 32 bits are rejected with a validation message.

What does a left shift do to a number?

A left shift (<<) moves all bits to the left by the specified amount, filling vacated positions on the right with 0s. Each single-position left shift is equivalent to multiplying by 2. For example, 0011 << 1 = 0110.

Binary Calculator

Binary arithmetic calculator with step-by-step workings

Updated Mar 2026100% Private — runs in browser

Binary Calculator

Arithmetic, bitwise operations, base conversion and ASCII encoding

Enter Number

Base

Binary (Base 2)0b11001010

Decimal (Base 10)202

Hexadecimal (Base 16)0xCA

Octal (Base 8)0o312

Bit Representations

8-bit1100 1010

16-bit0000 0000 1100 1010

32-bit0000 0000 0000 0000 0000 0000 1100 1010