Binary Number | Conversion - Electrical4u

 INTRODUCTION

The branch of electronics , which deals with digital circuits, it called digital electronics . the term digital reminds up of digital products can be attributed to low cost , good performance and rapid innovation in the field in the last few decades . Digital techniques have also replaced lots of older "Analog Circuit" used in consumer products such as, radio , T.V , etc.

Note 

In this series we read basic to Advance of Digital Electronics 

BINARY NUMBER SYSTEM

A number system is a code that used symbols to count numbers . The most common and familiar number system is "Decimal number system" The decimal number system used the symbol is 0 , 1 , 2 , 3 , 4 , 5 ,6 , 7 , 8 and 9 . Thus the decimal system used 10 digits for counting . A binary system used only two Digits 0 and 1 only . 

For example : 1001 , 111 , 0001 , all are binary number 

Every number system has placed value for every number 

For example : 482 in a decimal system is represented as - 4 × 10^2 + 8 × 10^1 + 2 × 10^0 

In similar way , a binary number also has a placed value for each digit . 

CONVERSION OF BINARY NUMBER INTO DECIMAL NUMBER 

To convert a binary number into its decimal equivalent some instruction are given below

1. Read the binary number from right to left and multiply each binary number  2⁰ , 2¹ , 2² , 2³ , 2⁴ , 2⁵ , 2⁶  and so on 

2. Add individual number . This will be decimal equivalent of the number . 

Now we practice some Question Based On Decimal Number 

Q1. Convert the Binary number ( 1101011 ) 2  into its decimal equation .

Solution - Read number Right to left and multiplying digits with increasing power of 2 , we found 

1 × 2⁶ + 1 × 2⁵ + 0 × 2⁴ + 1 × 2³ + 0 × 2² + 1 ×  2¹ + 1 × 2⁰

= 64 + 32 + 0 + 8 + 0 + 2 + 1 

= 107 

Q2. convert ( 1101.11 )2 into decimal equivalent 

Solution - we can solute into two part of this question 

(1101.12)2 = ( 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰ ) + ( 1 × 2-¹ + 1 × 2-²)

= ( 8 + 4 + 0 + 1 ) + ( 0.5 + 0.25 )

= 13.75

Note 

If  binary number is in decimal , then , read from left to right and multiplying by (-ve power) show above question