Number System including Binary

There are four types of number system.

1.   Binary (base 2) = 0,1

2.   Octal (base 8) = 0,1,2,3,4,5,6,7

3.   Decimal (base 10) = 0,1,2,3,4,5,6,7,8,9

4.   Hexadecimal (base 16) =0,1,2,3,4,5,6,7,8,9,A,B,C,D

1.   Binary coded decimal (BCD)

Decimal number system is convert into binary number system which is called BCD.

When decimal number system 28 is convert into BCD it became 00101000.



Change binary number into decimal number:

EG: 100111

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………



1*25+0*24+0*23+1*22+1*21+1*20

= 32+0+0+4+2+1

= 39

(100111)2 = (39)10





(1011)2 = (11)10

= 1*23+0*22+1*21+1*20

= 8+0+2+1

= 11



   (10)                    (2)                       (8)                     (16)

Decimal             Binary                octal          hexadecimal

       0                     0000                      0                       0

       1                     0001                      1                        1

       2                    0010                      2                        2

       3                        11                        3                        3

       4                     100                       4                        4

       5                      101                       5                        5

       6                      110                       6                        6

       7                      111                       7                        7

       8                     1000                      8                        8

       9                     1001                      9                        9

      10                    1010                      A                        A

      11                    1011                      B                        B

      12                    1100                      C                        C

      13                   1101                      D                       D

      14                  1110                      E                        E

      15                    1111                     F                       F



Decimal to binary

          (43)10

                                                                 32     16     8     4     2     1

                                                                  25        24         23    22   21    2

Steps breaking into multiples of 2 = 1       0       1      0    1     1

(43)10 = (101011)2      or by divide by 2

(43)10                                                              remainder

43/2 = 21                                                         1

21/2 = 10                                                          1

10/2 = 5                                                             0

5/2 = 2                                                               1

2/2 = 1                                                               0

½ = 0                                                                   1

Ans:101011                                                     



(39)10                                                         remainder

39/2 = 19                                                          1

19/2 = 9                                                             1

9/2 = 4                                                               1

4/2 = 2                                                               0

2/2 = 1                                                               0

½ = 0                                                                   0

Ans:100111



(11)10 = 1011

11/2 = 5                      1

5/2 = 2                         1

2/2 = 1                         0

½ =0                             1

1.   D TO B

 

Divide the given no. by RHS base and draw an arrow from bottom on top.

EG: Convert (14)10 = (?)2

Thus (14)10 = (1110)2       

2.   B TO D

Multiply the given no. by L.H.S base value with power from right to left and the results.

EG. Covert (1110)2 = (?)10    

 Place value =      23                22               21               20     

    Binary digits=      1                  1                 1                 1

Conversion =   (1*8)    +    (1*4)    +   (1*2)   + (0*2)

               = 8+4+2+0

               = 14

3.   B TO O 

Make a group of 3 bite from left to right of given binary digits and represent it by octal equivalent.

EG:(100111101)2 = (?)8

Binary no.2                100            111            101

Octal equal8                 4                 7                 5

Thus  (10011101)2 = (475)8

4.   B TO H

Make a group of 4 bits from left to right of given binary digits and represent it by hexadecimal equivalent.

EG: (101010011110)2 = (?)16

                              1010                    1001                    1110

Binary no.2           1010                   1001                   1110

Hex. Eq.                     A                          9                          E

(101010011110)2 = (A9E)16

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