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Binary Calculator & Bitwise Logic Solver

Perform binary arithmetic and bitwise logic operations with hex and decimal conversions.

Quick Answer:Enter two binary strings (0s and 1s) and choose an operator (+, -, *, AND, OR, XOR). The tool computes the binary, decimal, and hex outputs.

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How to Use the Binary Calculator: Bitwise & Arithmetic Operations

1Enter your first binary number string (containing only 0s and 1s).
2Choose your operation (+, -, *, AND, OR, or XOR).
3Enter your second binary number string.
4View the calculated binary result alongside decimal (base 10) and hexadecimal representations.

Formula & How It Works

Base-2 Positional & Bitwise Logic Equations

Binary = ∑(d_i × 2^i); Bitwise AND: 1&1=1; Bitwise OR: 0|0=0; Bitwise XOR: 1^1=0, 1^0=1

Performs integer parsing and bitwise manipulations using bitmask logic.

Worked Examples

Adding 1010 (10) and 0101 (5)

Input: 1010 + 0101

Explanation: Binary carry addition: 10 + 5 = 15, which is 1111 in base 2.

Result: 1111 (Decimal: 15, Hex: 0xF)

Frequently Asked Questions

How does binary addition work?▼

0+0=0, 0+1=1, 1+0=1, and 1+1=0 with a carry of 1 to the next higher positional bit.

What is the difference between AND and OR operators?▼

AND produces a 1 only when both corresponding bits are 1; OR produces a 1 when at least one corresponding bit is 1.

What is the XOR (exclusive OR) operation?▼

XOR produces a 1 if and only if the two input bits differ (one is 0 and the other is 1).

Why is hexadecimal commonly paired with binary?▼

Each hexadecimal digit corresponds to 4 binary bits (a nibble), making byte reading human-friendly.

Quick Reference & Conversion Table

Decimal	Binary (4-Bit)	Hexadecimal	Octal
0	0000	0x0	0
5	0101	0x5	5
10	1010	0xA	12
15	1111	0xF	17

⚠️ Common Pitfalls to Avoid

•Entering characters other than 0 and 1 in binary fields.
•Confusing bitwise OR (which yields 1 if either bit is 1) with bitwise XOR (which yields 0 if both bits are 1).