Tue. Jul 16th, 2019

# Converting Decimal, Binary, Octal, Hexadecimal

Digital Systems uses a variety of different number systems, (e.g. Decimal, Hexadecimal, Octal, Binary). A number system is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems.

## Numeral Systems Conversion Table

Decimal Base-10
Binary Base-2
Octal Base-8
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

The examples of the Decimal, Binary, Octal and Hexadecimal number systems are described below:

### Decimal Number System (Base 10):

Decimal numbers use digits from 0 to 9

Example:

253810 = 2×103+5×102+3×101+8×100

### Binary Number System (Base 2):

Binary Numbers uses only 0 and 1 digits

Example:

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

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

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

### Octal Number System (Base 8):

Octal numbers use digits from 0 to 7

Example:

278 = 2×81+7×8= 16+7 = 23

308 = 3×81+0×8= 24

43078 = 4×83+3×82+0×81+7×80= 2247

### Hexadecimal Number System (Base 16)

Hexa numbers use digits from 0 to 9 and A to F

Example:

2816 = 28 = 2×161+8×16= 40

2F16 = 2F = 2×161+15×16= 47

BC1216 = BC12 = 11×163+12×162+1×161+2×160= 48146