How to Calculate Binary Decimal
What is Binary Decimal?
A binary to decimal (and decimal to binary) converter translates between base 2 and base 10. Binary is the native language of digital computers; decimal is the human number system.
Formula
Binary to decimal: Σ (bit value × 2^position); Decimal to binary: repeatedly divide by 2, read remainders in reverse
- b
- Binary digit (0 or 1)
- d
- Decimal value
- n
- Bit position (rightmost = 0)
Step-by-Step Guide
- 1Binary to decimal: each bit position = 2ⁿ, sum the 1-positions
- 2Decimal to binary: divide by 2 repeatedly, read remainders in reverse
- 38-bit byte: values 0–255; 16-bit: 0–65,535
- 4Signed integers use two's complement for negative numbers
Worked Examples
Input
Binary 11001010
Result
128+64+0+0+8+0+2+0 = 202 decimal
Frequently Asked Questions
Why do computers use binary?
Binary matches the on/off states of transistors in circuits. 1 = on/high voltage, 0 = off/low voltage.
What is a byte?
A byte is 8 bits. It can represent values from 0 (00000000) to 255 (11111111).
How are negative numbers represented?
Two's complement: flip all bits and add 1. Example: −5 as 8-bit = 11111011.