Number systems define how we write and interpret numeric values. While humans count in decimal (base 10), computers process binary (base 2). Programmers frequently use hexadecimal (base 16) as a compact binary shorthand, and octal (base 8) still appears in Unix permissions and legacy systems. This guide explains each system, conversion methods, and links to free Numverto tools and reference tables.
Decimal (Base 10)
Decimal is our everyday system using digits 0–9. Each position represents a power of 10: hundreds, tens, ones. The number 429 means (4×100)+(2×10)+(9×1). All other bases follow the same positional logic with a different radix.
Binary (Base 2)
Binary uses only 0 and 1. Each bit doubles the place value: …8, 4, 2, 1. Example: 1011₂ = 8+2+1 = 11₁₀. Binary is fundamental to CPU registers, memory, networking bits, and logic gates. See our binary table (0–255) and binary explained article.
Octal (Base 8)
Octal digits run 0–7. Each octal digit maps to three binary bits. Example: 13₈ = 1×8 + 3 = 11₁₀. Unix chmod 755 means owner rwx (7), group rx (5), others rx (5). Read the octal conversion guide.
Hexadecimal (Base 16)
Hex uses 0–9 and A–F (10–15). One hex digit = four binary bits. Colour #FF5733, memory address 0x7FFF, and machine code dumps all use hex. Browse the hexadecimal table.
Conversion Methods Summary
Any Base → Decimal
Multiply each digit by (base^position) and sum. Position 0 is the rightmost digit.
Decimal → Any Base
Repeatedly divide by the target base; remainders read bottom-to-top form the result.
Binary ↔ Hex
Group binary in 4-bit nibbles; convert each nibble to one hex digit (fastest method for large numbers).
Free Numverto Tools
- Number System Converter — all four bases instantly
- Binary Arithmetic — add, subtract, multiply in binary
- BCD Converter — decimal ↔ binary coded decimal
- ASCII Converter — text ↔ character codes
- 1's & 2's Complement — signed binary representation
- IEEE 754 Converter — floating-point bit layout