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
1. Decimal system: This is the system which we use in daily life

Value of b=10

e.g.  (456)10

= 4*102 + 5*101 + 6* 100

The weights of the corresponding bits for decimal system are as

 104 103 102 101 100 . 10-1 10-2 10000 1000 100 10 1 . 0.10 0.01 MSB Decimal point

1. Binary system: This is number system which is used to represent values in the digital environment. Here value of b=2

(11101.01)2

=1*24 + 1 *23 + 1 * 22 + 0 *21 + 1 * 20+ 0 *2-1 + 1 * 2-2

= (29.25)10 so number given is equal to 29 in decimal.

Representing large values in binary system may be very cumbersome and also it’s very difficult to a human to work with such large values in binary as it require 3 to 4 time more digits than for decimal system for same value e.g. 10101111011101112.Hence the number systems like octal and hexadecimal systems are developed just to simplify this. Corresponding equivalents of the value above in octal and hexadecimal are 1275678 and AF7716  that are easier to read and remember for engineers and other technicians

The weights of the corresponding bits for binary system are as

 24 23 22 21 20 . 2-1 2-2 16 8 4 2 1 . 0.50 0.25 MSB Decimal point

However, any series of 1’s and 0’s is not binary number. Sometimes it may represent some other information like some binary codes as gray code, parity bit numbers etc

Binary number formats:

1. Bit: It is defined as smallest unit of data. Eg. 0, 1

2. Nibble: It is a combination of 4 bits Eg. 0000, 1010, 1000, 0100 etc

3. Byte: A byte is a combination of 8 bits Eg. 0010 1010—it has 2 nibbles

4. Word: it is defined as combination of 16 bits Eg. 0010 0011 0111 1111 – it has 4 nibbles or 2 bytes

5. Double word: It is defined as combination of 32 bits.Eg. 0010 0011 0111 1111 0010 0011 0111 1111 it has 8 nibbles or 4 bytes