Programmer Utility

Bitwise Calculator

Evaluate integer bitwise operations and inspect two’s complement views across bit widths for practical debugging and systems work.

Bitwise Input

Result

How to use

Enter integer values for A and B.
Choose a bitwise operation and bit width view.
Calculate to see decimal output and binary representation.

How bitwise operations work

Bitwise operators compare bits position-by-position. For example, AND returns 1 only when both compared bits are 1. Shift operations move bits left or right, changing numeric value by powers of two.

Quick examples

42 AND 15 → 10
8 << 2 → 32

FAQ

What does two’s complement show?

It shows the signed binary representation within the chosen bit width.

Can I use negative numbers?

Yes, signed integers are supported and represented using two’s complement display.

Why does NOT ignore input B?

NOT is unary, so it only applies to input A by definition.

Concept overview

Where bitwise logic is used

Bitwise operators are core tools in systems programming, protocol parsing, cryptography helpers, and graphics pipelines. They let you set flags, mask values, and transform integers with predictable low-level behavior.

This page also includes set-bit count and two’s complement output, so you can inspect both the numeric result and its binary representation in a selected width.

Operation notes

AND keeps bits set in both operands.
OR keeps bits set in either operand.
XOR keeps bits that differ.
NOT flips all bits in the integer representation.

Manual walkthrough

Example: 13 XOR 10

Write binary forms: 13 = 1101, 10 = 1010
XOR bit by bit: 1101 ⊕ 1010 = 0111
Convert back to decimal: 0111 = 7

Use this manual pattern for sanity checks when implementing masks, permissions, and compact state flags.

Common errors and fixes

Decimal vs binary confusion → remember inputs are decimal integers by default.
Unexpected negative representation → check selected bit width and two’s complement result.
Shift count mistakes → verify B is the intended shift amount.

Extended FAQ

Bitwise calculator questions

Does bit width change the decimal result?

The direct computed integer stays the same; width affects the displayed two’s complement representation.

How is set-bit count calculated for negatives?

The utility currently counts bits from absolute magnitude, not finite-width signed encoding.

Can I model flag checks with this tool?

Yes. AND and XOR are especially useful for flag masking and toggling scenarios.

Why does left shift grow fast?

Each left shift by one position multiplies the value by 2 in integer arithmetic.

What should I pair with this tool?

Use Base Converter to inspect values in hex/binary before or after bitwise operations.