Page 83 - Electrician - TT (Volume 2)

ELECTRICIAN - CITS

Binary numbers, logic gates and combinational circuits

Objectives: At the end of this lesson you shall be able to
• explain the digital electronics principle and positional notation and weightage
• explain decimal to binary conversion, binary odometer
• explain hexadecimal number system
• convert decimal to hexa, hexa to decimal and BCD system
• explain logic gates principle - NOT, OR and AND gates with truth table
• explain combinational gates - NAND, NOR with truth table and logic pulser.

Introduction
When we hear the word 'number' immediately we recall the decimal digits 0,1,2....9 and their combinations. Digital
circuits do not process decimal numbers. Instead, they work with binary numbers which use the digits '0' and '1'
only. The binary number system and digital codes are fundamental to digital electronics. But people do not like
working with binary numbers because they are very long when representing larger decimal quantities. Therefore
digital codes like octal, hexadecimal and binary coded decimal are widely used to compress long strings of binary
numbers.
Binary number systems consists of 1s and 0s. Hence this number system is well suited for adopting it to the digital
electronics.
The decimal number system is the most commonly used number system in the world. It uses 10 different characters
to show the values of numbers. Because this number system uses 10 different characters it is called base-10
system. The base of a number system tells you how many different characters are used. The mathematical term
for the base of a number system is radix.

The 10 characters used in the decimal number systems are 0,1,2,3,4,5,6,7,8,9.
Positional notation and weightage
A decimal integer value can be expressed in units, tens, hundreds, thousands and so on. For example decimal
number 1967 can be written as 1967 = 1000 + 900 + 60 + 7. In powers of 10, this becomes.
————————————— 1 x 10 = 1000
3
10 10 10 10 9 x 10 = 900
0
1
2
3
2
—————————————— 6 x 10 = 60
1
1 9 6 7 7 x 10 = 7
0
—————————————— ———
1967
i.e. [1967]10 = 1(103) + 9(102) + 6(101) + 7(100)
This decimal number system is an example of positional notation. Each digit position has a weightage. The
positional weightage for each digit varies in the sequence 100, 101, 102, 103 etc starting from the least significant
digit.
The sum of the digits multiplied by their weightage gives the total amount being represented as shown above.
In a similar way, binary number can be written in terms of weightage.
To get the decimal equivalent, then the positional weightage should be written as follows.

[1010] = 1(2 ) + 0(2 ) + 1(2 ) + 0(2 )
0
1
3
2
2
= 8 + 0 + 2 + 0
[1010] = [10] 10
2

70

CITS : Power - Electrician & Wireman - Lesson 60-69