NUMBER SYSTEM

NUMBER SYSTEM

It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
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The four most common number system types are:

• Decimal number system (Base- 10)
• Binary number system (Base- 2)
• Octal number system (Base-8)
• Hexadecimal number system (Base- 16)           

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

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

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