Numeral systems

• Numeral system
• Binary numeral system
• Octal numeral system
• Decimal numeral system
• Hex Numeral system
• Numeral system conversion table

Numeral system

b - numeral system base

d_n - the n-th digit

n - can start from negative number if the number has a fraction part.

N+1 - the number of digits

Binary Numeral System - Base-2

Binary numbers uses only 0 and 1 digits.

B denotes binary prefix.

Examples:

10101₂ = 10101B = 1×2⁴+0×2³+1×2²+0×2¹+1×2⁰ = 16+4+1= 21

10111₂ = 10111B = 1×2⁴+0×2³+1×2²+1×2¹+1×2⁰ = 16+4+2+1= 23

100011₂ = 100011B = 1×2⁵+0×2⁴+0×2³+0×2²+1×2¹+1×2⁰ =32+2+1= 35

Octal Numeral System - Base-8

Octal numbers uses digits from 0..7.

Examples:

27₈ = 2×8¹+7×8⁰ = 16+7 = 23

30₈ = 3×8¹+0×8⁰ = 24

4307₈ = 4×8³+3×8²+0×8¹+7×8⁰= 2247

Decimal Numeral System - Base-10

Decimal numbers uses digits from 0..9.

These are the regular numbers that we use.

Example:

2538₁₀ = 2×10³+5×10²+3×10¹+8×10⁰

Hexadecimal Numeral System - Base-16

Hex numbers uses digits from 0..9 and A..F.

H denotes hex prefix.

Examples:

28₁₆ = 28H = 2×16¹+8×16⁰ = 40

2F₁₆ = 2FH = 2×16¹+15×16⁰ = 47

BC12₁₆ = BC12H = 11×16³+12×16²+1×16¹+2×16⁰= 48146

Numeral systems conversion table