Bitwise Operations (AND, OR, XOR, NOT & Bit Shifts) Calculator

Inspect bitwise logic gates and bit-shift arithmetic on non-negative integers.

Bitwise XOR (A ^ B)
37
Bitwise AND (A & B) 10
Bitwise OR (A | B) 47
Left Shift (A << 2) 168
Right Shift (A >> 2) 10
Inputs
First unsigned integer operand A.
Second unsigned integer operand B.
Bit shift count k for A << k and A >> k.
Results & Graph
Bitwise XOR (A ^ B)
37
Bitwise AND (A & B)
10
Bitwise OR (A | B)
47
Left Shift (A << 2)
168
Right Shift (A >> 2)
10

Bitwise XOR (A ^ B)

Graph 1 • Int A Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 31.9 63.7 50%: 26 26 50% 75%: 16 16 75% 100%: 37 37 100% 125%: 59 59 125% 150%: 48 48 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Bitwise XOR (A ^ B) 37 Bitwise AND (A & B) 10 Bitwise OR (A | B) 47 Left Shift (A << 2) 168
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Bitwise XOR (A ^ B)37Bitwise AND (A & B)10Bitwise OR (A | B)47Left Shift (A << 2)168Right Shift (A >> 2)10
Summary: For A = 42 and B = 15: A & B = 10, A | B = 47, A ^ B = 37, and A << 2 = 168.
Summary: For A = 42 and B = 15: A & B = 10, A | B = 47, A ^ B = 37, and A << 2 = 168.

Formula & Mathematical Methodology: Bitwise Operations Mathematical Identity

XOR = (A | B) − (A & B)
HammingDistance = popcount(A ^ B)
XOR = (A | B) − (A & B); HammingDistance = popcount(A ^ B)
  • intA: Int A (numeric parameter)
  • intB: Int B (numeric parameter)
  • shiftBits: Shift Bits (numeric parameter)

Rounding: All calculations run in double-precision IEEE-754 arithmetic; displayed outputs round to up to 4 decimal places.

Worked Example: Worked Mathematical Verification: Bitwise Operations

Inspect bitwise logic gates and bit-shift arithmetic on non-negative integers.

  1. Verify the domain constraints of the input parameters.
  2. Apply the governing mathematical identity: XOR = (A | B) − (A & B); HammingDistance = popcount(A ^ B).
  3. Cross-check the primary value against the supporting invariants and coordinate graph.
Result: Evaluates Bitwise Operations via XOR = (A | B) − (A & B); HammingDistance = popcount(A ^ B).

Frequently Asked Questions

What mathematical formula does the Bitwise Operations (AND, OR, XOR, NOT & Bit Shifts) Calculator use?

It directly evaluates XOR = (A | B) − (A & B); HammingDistance = popcount(A ^ B) in double-precision floating-point arithmetic and updates all supporting invariants and graphs live.

How can I compare different parameter sets?

Click Compare in the results toolbar to pin up to three parameter combinations side by side.

Can I export the mathematical report or share a link?

Yes. Use the Share Link, Copy Summary, or Markdown/JSON export buttons in the results panel.

Mathematics & Statistics • Discrete Math & Logic Guide

How to Use the Bitwise Operations (AND, OR, XOR, NOT & Bit Shifts) Calculator: Practical Guide & Visual Analysis

Compute 32-bit integer bitwise AND (A & B), bitwise OR (A | B), bitwise XOR (A ^ B), left shift, right shift, and Hamming distance. Includes textbook mathematical notation, step-by-step verification, and three custom SVG visualizations. Whether you are researching bitwise operations (and, or, xor, not & bit shifts) calculator, bitwise operations, bitwise and or xor shift, discrete math & logic calculator, this interactive tool helps you compute 32-bit integer bitwise AND (A & B), bitwise OR (A | B), bitwise XOR (A ^ B), left shift, right shift, and Hamming distance.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust Int A, Int B, Shift Bits, the calculator immediately computes Primary exact or numerical solution, Supporting identities & invariants, 3-Panel mathematical SVG plots and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Universal Mathematical & Statistical Standard (ISO 80000-2))

In our benchmark scenario (Worked Mathematical Verification: Bitwise Operations), Evaluates Bitwise Operations via XOR = (A | B) − (A & B); HammingDistance = popcount(A ^ B). Keep in mind that uses standard Euclidean geometry, real/complex algebra, and NIST statistical definitions. For related calculations in Mathematics & Statistics, explore Scientific Calculator, Statistics & Standard Deviation Calculator, Geometry Calculator (Right Triangle, Circle & Cylinder).