NUMBER SYSTEM

 

Number System

 

Number system	Base	Values
Decimal Number System	10	0,1 2 3 4 5 6 7 8 9
Binary Number System	2	0 1
Octal Number System	8	0 1 2 3 4 5 6 7
Hexadecimal Number System	16	0 -9 A - F

 

The number system having base of 10 and values of 0 to 9 is called decimal number system.

 

 

1.     Converstion

Decimal to binary, octal, hexadecimal

Binary to decimal, octal, hexa

Octal to binary, decimal, Hexadecimal

hexaD to Decimal, binary, octal

 

Case No. 1

Decimal to binary or octal or hexadecimal = divide

  For    example: 104 to binary

2	104	0
2	52	0
2	26	0
2	13	1
2	6	0
2	3	1
	1

(104)₁₀ = (1101000)

 

Any to decimal = multiply

11011 into decimal

 

11011

1*2⁴+1*2³+0*2²+1*2¹+1*2⁰

1*16 + 1*8 + 0 + 1*2 + 1*1

16+8+2+1

27

 

Case no 2

Decimal	binary	octal	Hexadecimal
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

 

 

100 110 101 4      6      5 100          110     101

1101110 INTO OCTAL

1 101 110

            156    

1     5      3

         001 101   011

 

 

 

 

1101110 into hexadecimal

 

110 1110

     6E

6          6

110 0110

 

110 0110

 

Case no 3

 

Octal to hexa decimal

4235

4          2          3          5

100     010     011     101

100010011101

 

 

Hex to octal

4235

4          2          3          5

0100  0010  0011  0101

100001000110101

100     001     000     110     101

4          1          0          6          5

 

 

 

C                      A                     F                      E

1100              0001              1111              1110

1100000111111110

 

2076 qn. (FA) ₁₆ into binary                     (420) ₁₀ into octal

                        111*10                                 1101/101

2075 qn. (217)₁₀ into binary                    (397)₁₆ into decimal

                        1011*11                               110111-11001