How to Calculate Number Base Full
What is Number Base Full?
Number bases (or radices) define how many digits a counting system uses. Decimal (base-10) uses 0–9, binary (base-2) uses 0–1, octal (base-8) uses 0–7, and hexadecimal (base-16) uses 0–9 and A–F.
Formula
Base conversion: Decimal = d₀×b⁰ + d₁×b¹ + d₂×b² + ... where b is the base
- b
- Numeric Base (integer)
- d
- Digit Value (0 to b-1)
- n
- Position (index)
Step-by-Step Guide
- 1Binary to decimal: each bit × 2^position, sum all
- 2Decimal to binary: divide by 2, collect remainders
- 3Hex digits 0–9 = values 0–9; A–F = values 10–15
- 4Base-16 is compact: each hex digit = 4 binary bits
Worked Examples
Input
Binary 1010
Result
1×8+0×4+1×2+0×1 = Decimal 10 = Hex A
Input
Decimal 255
Result
Binary 11111111 = Hex FF
Frequently Asked Questions
Why do computers use binary?
Binary (base 2) uses only 0 and 1, which correspond to electrical states (off/on). This makes hardware simple and reliable.
What is hexadecimal used for?
Hexadecimal (base 16) compactly represents binary data. Each hex digit represents 4 binary digits, making it ideal for memory addresses and color codes.
How do I convert between bases?
To convert to decimal, use positional notation. To convert from decimal, repeatedly divide and collect remainders, reading bottom-to-top.