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 SUB. using (r-1)'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