Compute binary operations and base-2 conversions reliably.
Overview
Binary is the core language of digital systems because every bit can be represented by two stable states, 0 and 1. Processors, memory, and logic gates all rely on this representation.
Many errors in binary math come from carrying and borrowing rules that differ from base-10 habits. A binary calculator helps validate bit-level operations used in coursework, programming, and embedded debugging.
This tool handles addition, subtraction, multiplication, and conversion between binary and decimal forms. It is useful for checking masks, packet fields, and intermediate arithmetic in algorithm design.
Steps
Select arithmetic or conversion mode.
Type values using only digits 0 and 1.
The tool applies base-2 rules automatically.
Review step output to verify each bit transition.
Translate result to decimal or hexadecimal for reporting.
Math
Decimal value = sum(bit_i x 2^i); Binary addition uses carry when 1 + 1 = 10_2
Each bit position has weight 2^i. Arithmetic works like place-value math but with base 2, so carries occur at value 2 rather than 10.
Worked cases
1011 + 0110 = 10001
Sum = 10001 (17 decimal).
1x32 + 1x16 + 0x8 + 1x4 + 0x2 + 1x1
Decimal = 53.
45 = 32 + 8 + 4 + 1
Binary = 101101.
Why use this
Questions