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Digital Electronics
NUMBER SYSTEM
INTRODUCTION
DECIMAL & BINARY SYSTEM
OCTAL & HEXADECIMAL SYSTEM
DECIMAL to BINARY CONVERSION
DECIMAL to OCTAL & HEXADECIMAL
BINARY to OCTAL & HEXADECIMAL and vice versa
ADDITION
SUBTRACTION
MULTIPLICATION & DIVISON
COMPLIMENTS
SUBTRACTION using r's COMPLIMENTS
BINARY CODES
BOOLEAN ALGEBRA
K MAPS
COMBINATIONAL CKT
SEQUENTIAL CIRCUITS
TIMING CIRCUITS

 

 

Octal system: b=8

(407)8

= 4 * 82 + 0 *81 + 7 * 80

= (261)10

Similarly 24.68 = 2 x (81) + 4 x (80) + 6 x (8-1) = 20.7510

11.18 = 1 x (81) + 1 x (80) + 1 x (8-1) = 9.12510

 

The weights of the corresponding bits for octal system are as

84

83

82

81

80

.

8-1

8-2

4096

512

64

8

1

.

0.125

0.015625

MSB

 

 

 

 

Decimal point

 

 

 

2. Hexadecimal system: b=16                         {value of A=10, B=11, C=12, D=13, E=14, F=15}

(A0F) 16

= A * 162 + 0 *161 + F *160

= 10 * 162 + 0 *161 + 15 *160

=2560 + 15

= (2575) 10

Similarly 11.116 = 1 x (161) + 1 x (160) + 1 x (16-1) = 17.062510

 12.316 = 1 x (161) + 2 x (160) + 3 x (16-1) = 18.187510

 

The weights of the corresponding bits for hexadecimal system are as

 

164

163

162

161

160

.

16-1

16-2

65536

4096

256

16

1

.

0.125

0.015625

MSB

 

 

 

 

Decimal point

 

 

               

 

 

Corresponding equivalents of decimal 0-15 in Binary, octal & hexadecimal system

 

Decimal                                Binary                   Octal                      Hexadecimal     

 0                             0000                      00                           0

 1                              0001                      01                           1           

 2                             0010                      02                           2    

 3                             0011                      03                           3 

 4                             0100                      04                           4             

 5                             0101                      05                           5     

 6                             0110                      06                           6        

 7                             0111                      07                           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              15               1111                      17                           F        

          

 

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