Page 7 - Digital Electronics by harish

UNIT - I
NUMBER SYSTEM AND BOOLEAN ALGEBRA

1.1 NUMBER SYSTEMS AND BINARY CODES
1.1.1 Number systems

Number systems other than the familiar decimal (base 10) number system are used in the
computer field and digital systems. Digital computers internally use the binary (base 2)
number system to represent data and perform arithmetic calculations. The hexadecimal
(base 16) number system is a shorthand method of working with binary numbers. The octal
(base 8) number system is also less commonly used in digital computers.

The different number systems are:
1. Decimal number system
2. Binary number system
3. Octal number system and
4. Hexadecimal number system

Decimal number system

We use the decimal number system in our day-to-day life for representing numbers. It is a
positionalnumber system. It has ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base (or radix,
or weight) of the decimal number system is 10. The place value of each position is given
below:

1
0
3
2
-1
-2
-3
10 10 10 10 . 10 10 10
1000 100 10 1 . 0.1 0.01 0.001

Example:

-2
1
0
-1
3
2
3472.65 = 3 x 10 + 4 x 10 + 7 x 10 + 2 x 10 + 6 x 10 + 5 x 10
= 3 x 1000 + 4 x 100 + 7 x 10 + 2 x 1 + 6 x 0.1 + 5 x 0.01

Symbols used: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Base (or radix, or weight): 10
-1
3
2
0
1
-3
-2
Place value: ….. 10 , 10 , 10 , 10 . 10 , 10 , 10 …..

Binary number system

Binary number system is used in computers and digital circuits for representing numbers. It
has only two symbols: 0 and 1. The base (or radix, or weight) of the binary number system is
2. The place value of each position is given below:

0
2
3
-1
-2
-3
1
2 2 2 2 . 2 2 2
8 4 2 1 . 0.5 0.25 0.125

Example:

-2
-1
3
1
2
0
1011.01 = 1 x 2 + 0 x 2 + 1 x 2 + 1 x 2 + 0 x 2 + 1 x 2
= 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1 + 0 x 0.5 + 1 x 0.25
= 11.25 (in decimal)

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