# Conversion of Number System

#### Conversion of Number System

1. ##### Decimal Number System to Binary Number System:-

(25.625)10 = (X)2

For 25

Output  Remainder

25 / 2 = 12      1

12 / 2 = 6       0

6 / 2 = 3        0

3 / 2 = 1        1

1 / 2 = 0       1

For conversion arrange the remainder from bottom to top order.

Therefore RESULT for 25 is (11001)2

For fraction part .625 , we follow given procedure:-

 0.625*2=1.250 integer part =1 0.250*2 = 0.500 integer part =0 0.500*2 = 1.000 integer part =1

For conversion arrange the Integer Part from top to bottom order.

Therefore RESULT is .1012

1. #### Decimal Number System to Octal Number System:-

(25.40)10 = (X)8

For 25

Output  Remainder

25 / 8 = 3       1

3 / 8 = 0        3

For conversion arrange the remainder from bottom to top order.

Therefore RESULT for 25 is (31)8

For fraction part .40, we follow given procedure:-

 0.40*8=3.20 integer part =3 0.20*8 = 1.60 integer part =1 0.60*8 = 4.80 integer part =4 0.80*8 = 6.40 integer part =6

For conversion arrange the Integer Part from top to bottom order.

Therefore RESULT is (.3146)8

1. #### Decimal Number System to Hexadecimal Number System:-

(590.0628)10 = (X)16

For 25

Output    Remainder

590 / 16 = 36      14(E)

36 / 16 = 2        4

2 / 16 = 0         2

For conversion arrange the remainder from bottom to top order.

Therefore RESULT for 25 is (24E) 16

For fraction part .40, we follow given procedure:-

 0.0628*16=1.0048 integer part =1 0048*16 = 0.0768 integer part =0 0768*16 = 1.2288 integer part =1 2288*16 = 3.6608 integer part =3

For conversion arrange the Integer Part from top to bottom order.

Therefore RESULT is (.1013)16

1. #### Binary Number System to Decimal Number System:-

(1101.101)2 = (X)10

(1   1   0   1. 1    0    1)2

↑  ↑   ↑   ↑   ↑   ↑    ↑
22222-1   2-2    2-3

= (1x 23  +1x 22  0x 21  +1x 20 ) . ( 1 x 2-1 + 0 x 2-2 +1 x 2-3 )

= (8+4+0+1).(0.50+0.25+0.125)

=  (13 .875) 10

1. #### Octal Number System to Decimal Number System:-

(121.12)8 = (X)10

(1    2   1.  1     2  )8

↑   ↑   ↑   ↑     ↑
8880   8-1   8-2

= (1x 82 + 2x 81 +1x 80) . (1 x 8-1 + 2 x 8-2)

= (64+16+8).(0.125+0.03125)

=  (88 .15625) 10

1. #### Hexadecimal Number System to Decimal Number System:-

(1A.B1)16= (X)10

(1    A.       B     1  )2

↑    ↑        ↑     ↑
16160   16-1   16-2

= (1x 161 + 10x 160). (11 x 16-1 +1 x 16-2)

= (16+10). (0.6875+0.0039)

= (26 .6914) 10

1. #### Octal Number System to Binary Number System:-

(42.65)8 = (X)2

(4         2.       6      5  )2

↑       ↑        ↑      ↑

100   010     110    101

1. #### Binary Number System to Octal Number System:-

(11101.1111)2 = (X) 8

(0 1 1 1 0 1. 1 1  1 1 0 0  )2

↑       ↑        ↑       ↑

3       5        7      4

1. #### Hexadecimal Number System to Binary Number System:-

(42A.65B)8 = (X)2

( 4         2        A.       6           5        B)2

↑        ↑        ↑        ↑          ↑       ↑

0100   0010    1010   0110    0101   1101

1. #### Binary Number System to Hexadecimal Number System:-

(11101.11111)2 = (X)16

(0 0 0 1 1 1 0 1. 1 1  1 1 1 0 0 0 )2

↑          ↑           ↑          ↑

1          D          F          8

1. #### From Any Number System to Any other Number System:-

(435)6 = (X)4

For this firstly convert base 6 number system into decimal number system. Then convert decimal number system to Base 4 number system.

(4     3      5) 6

↑       ↑       ↑

62      61      6= (4x 62 +3x 61 + 5x 60)= (165) 10Now convert 165 to base 4.

Output  Remainder

165 / 4 = 41     1

41 / 4 = 10      1

10 / 4 = 4       2

2 / 4 = 0        2