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

Answer is:- (25.625)₁₀ = (11001.101)₂

 

2. 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

Answer is:- (25.40)₁₀ = (31.3146)₈

3. 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

Answer is:- (590.0628)₁₀ = (24E.1013)₁₆ 

4. Binary Number System to Decimal Number System:-

       (1101.101)₂ = (X)₁₀

₌   (1   1   0   1. 1    0    1)₂

↑  ↑   ↑   ↑   ↑   ↑    ↑
      2³  2²  2¹  2⁰  2^-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

↑   ↑   ↑   ↑     ↑
       8²  8¹  8⁰   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

2. Hexadecimal Number System to Decimal Number System:-

       (1A.B1)₁₆= (X)₁₀

₌   (1    A.       B     1  )₂

↑    ↑        ↑     ↑
      16¹  16⁰   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

3. Octal Number System to Binary Number System:-

 (42.65)₈ = (X)₂

(4         2.       6      5  )₂

↑       ↑        ↑      ↑

100   010     110    101  

Answer is:- (42.65)₈ = (100010.110101)₂

4. 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

Answer is:- (11101.1111)₂ = (35.74)₈

5. 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 

Answer is:- (42A.65B)₁₆ = (010000101010.011001011101)₂

6. 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

Answer is:- (11101.11111)₂ = (1D.F8)₁₆

7. 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      6⁰  = (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

Answer is:- (435)₆ = (2211)₄

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