Binary Calculator
Perform binary arithmetic and bitwise operations on values. Simulate CPU registers using signed Two's Complement configurations and view real-time conversions across bases.
Binary Output
1 0000
Multi-Base Representation Matrix
Bitwise Logic Inspector
Note: Visualizations show zero-padded numbers matching width magnitudes. In signed configurations, the far-left bit serves as the sign indicator (MSB).
Understanding Binary Operations & Registers
Binary is the foundational language of modern computer systems. While humans think in Base-10 (decimal), computers represent all instructions and states in Base-2 (binary) where bits are either 0 or 1. Our binary calculator allows you to perform low-level math and logic operations just like a computer processor.
Arithmetic vs. Bitwise Operations
This tool operates in two primary modes:
- Arithmetic Mode: Simulates standard binary addition, subtraction, multiplication, and division.
- Bitwise Mode: Directly executes bit-level logic such as AND, OR, XOR, NOT, and shifting operations. This is useful for masking bits, managing ports, or writing hardware protocols.
Two's Complement Signed Format
To represent negative numbers, computers use a convention called Two's Complement. In a fixed-bit depth (such as an 8-bit register), the highest-value bit (the far left bit) becomes negative. For instance, the binary string 11111111 is equal to -1. Our simulator lets you switch between Unsigned Arbitrary precision and signed 8-bit, 16-bit, and 32-bit registers to model registers accurately.
Frequently Asked Questions About Binary
How does Two's Complement work in this calculator?
Two's complement is a mathematical method used to represent signed negative integers in binary. The most significant bit acts as a negative weight.
Can this calculator perform bitwise operations?
Yes. Perform AND, OR, XOR, NOT, and bit shifts on signed/unsigned binary numbers.