Dec (10)
Bin (2)
Oct (8)
Hex (16)

What is Numeral System?

A Numeral System is a system of writing for expressing numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation to every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction, and division.

The following four basic Numeral Systems are commonly used:

  1. Decimal Numeral System (Base - 10)
  2. Binary Numeral System (Base - 2)
  3. Octal Numeral System (Base - 8)
  4. Hexadecimal Numeral System (Base - 16)

 

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

 

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

 

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

Decimal
(Base-10)
Binary
(Base-2)
Octal
(Base-8)
Hexadecimal
(Base-16)
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
16 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 23 13
20 10100 24 14
21 10101 25 15
22 10110 26 16
23 10111 27 17
24 11000 30 18
25 11001 31 19
26 11010 32 1A
27 11011 33 1B
28 11100 34 1C
29 11101 35 1D
30 11110 36 1E
31 11111 37 1F
32 100000 40 20