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CONVERSION BETWEEN DIFFERENT NUMBER SYSTEM

Conversion Decimal To Binary:
Steps:-
  • Divide the Decimal Number by 2
  • Get the remainder from step 1
  • Divide the quotient of the previous  by 2
  • Record the remainder from step 3.
  • Repeat step 3 and 4 for getting remainder until the quotient become 1 or 0.
  • write the quotient and remainder from last step to first step or from bottom to top.
Ex-  37 = (?)2
Sol:
2
37
R
2
18
1
2
9
0
2
4
1
2
2
0

1
0

(100101)2
Conversion Binary To Decimal:
Steps:-
  • Determine the position value of each digit
  • Multiply the postion value with by the corrosponding power of 2.
  • and Sum is the equivalent value in Decimal.
Ex- (100101)2
=1x25 + 0x24 + 0x23 + 1x22 + 0x21 + 1 x 20
=1x32 + 0x16 + 0x8 + 1x4 + 0x 2 + 1x 1
=32+0+0+4+1
= (37)10
(1011111)2=
= 1x26 + 0x25 + 1x24 + 1x23 + 1x22 + 1x21 + 1x20
=1x64 + 0x32 + 1x16 + 1x8 + 1x4 + 1x2 + 1x1
= 64+0+16+8+4+2+1
= (95)10
Conversion Decimal To Octal:
Steps:-

  • Divide the Decimal Number by 8
  • Get the remainder from step 1
  • Divide the quotient of the previous  by 2
  • Record the remainder from step 3.
  • Repeat step 3 and 4 for getting remainder until the quotient become 0 to 7(mean 0,1,2,3,4,5,6,7).
  • write the cosent and remainder from last step to first step or from bottom to top.
Ex-    
68)10= (?)8
8
68
R
8
8
4

1
0
(104)8
Conversion Octal To Decimal:
Steps:-
  • Determine the position value of each digit
  • Multiply the postion value with by the corrosponding power of 8.
  • and Sum is the equivalent value in Decimal.
Ex- (174)8
=1x82 + 7x81 + 4 x 80
=1x64+7x8+4x1
=64+56+4
= (124)10
Conversion Decimal To HexaDecimal
Steps:-
  • Divide the Decimal Number by 16.
  • Get the remainder from step 1.
  • Divide the quotient of the previous  by 16.
  • Record the remainder from step 3.
  • Repeat step 3 and 4 for getting remainder until the quotient become 0 to15.
  • write the quotient and remainder from last step to first step or from bottom to top.
  • Here Some Changes when we write Numbers, We Use A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
Ex-  (813)10=(?)16
Sol:
(813)10= (?)16
16
813
R
16
50
13

3
2

Here The Number Became 32-13 that mean (32D)16.
Conversion Decimal To HexaDecimal:
Steps:-
  • Determine the position value of each digit.
  • Here Some Changes when we write Numbers, We Use A for 10, B for 11, C for 12, D for 13, E for 14 and F for 15.
  • Multiply the postion value with by the corrosponding power of 16.
  • and Sum is the equivalent value in Decimal.
Ex- (3AF)8
=3x162 + Ax161 + F x 160
=3x162 + 10x161 + 15 x 160
=3x256+10x16+15x1
=768+160+15
= (943)10

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