Numeral Systems

Numeral System

b – numeral system base

dn – 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.

For example:

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11102 = 1110B = 1×24+1×23+1×22+0×21 = 16 + 8 + 4 = 28

111012 = 11101B = 1×24+1×23+1×22+0×21+1×2= 16 + 8 + 4 + 1 = 29

1011002 = 101100B = 1×25+0×24+1×23+1×22+0×21+0×20= 32 + 8 + 4 = 44

Octal Numeral System – Base-8

Octal numbers uses digits from 0..7.

For examples:

368 = 3×81+6×8= 24 + 6 = 30
508 = 5×81+0×8= 40
24038 = 2×83+4×82+0×81+3×80= 1024 + 256 + 24 = 1304

Decimal Numeral System – Base-10

Decimal numbers uses digits from 0..9.

These are the regular numbers that we use.

For example:

114210 = 1×103+1×102+4×101+2×100 = 1000 + 100 + 40 + 2 = 1142

Hexadecimal Numeral System – Base-16

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

H denotes hex prefix.

For examples:

1416 = 14H = 1×161+4×16= 16 + 4 = 20
3F16 = 3FH = 3×161+15×16= 48 + 15 = 63
CB1216 = CB12H = 12×163+11×162+1×161+2×160= 49152 + 2816 + 16 + 2 = 51986

Numeral systems conversion table

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