# Number System - Formulas, Examples, Shortcuts and Video

Number System Shortcuts - Page 2
Number System Important Questions - Page 3
Number System Video Lecture - Page 4

## NUMBER SYSTEM FACTS AND FORMULAS

A number system is nothing more than a code. For each distinct quantity there is an assigned symbol. The most familiar number system is the decimal system which uses 10 digits, that is, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The main advantage of its simplicity and long use. Most of the ancient societies used this system. Even in our everyday life we use this system and is sometimes being taken as the natural way to count. Since this system uses 10 digits it is called a system to base 10. A binary number system is a code that uses only two basic symbols, that is, 0 and 1. This system is very useful in computers. Since, in this system, only two symbols are there, it can be used in electronic industry using ‘on’ and ‘off’ positions of a switch denoted by the two digits 0 and 1.

Decimal Number System :
Decimal number system used 10 digits, 0 through 9, that is, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Binary Number System :
Binary means two. The binary number system uses only two digits, 0 and 1.

The basic or radix of a number system is equal to the number of digits or symbols used in that number system. For example, decimal system uses 10 digits, so that base of decimal system (this is, decimal numbers) is 10.

Binary numbers have base 2.
A subscript attached to a number indicates that base of the number. For example, $100_{2}$ means binary 100. $100_{10}$ stands for decimal 100.

Weights: In any number to a given base, each digit, depending on its position in the number has a weight in powers of the base.

Note: Decimal to Binary Conversion
Step 1 : Divide the number by 2.
Step 2 : Divide Quotient of Step 1 by 2.
Continue the process till we get quotient = 0 and remainder as 1.
Then, the remainder from down upwards written form left to right give the binary number.
Illustration 4 Convert decimal 23 to binary.
Solution Images
Reading the remainders upwards and writing from left to right we get the binary equivalent of decimal 23 as 10111.
That is, Binary 10111 is equivalent to decimal 23 or we can write $10111_{2}=23_{10}$ .

Note : Binary to Decimal Conversion
Following steps are involved to convert a binary number to its decimal equivalent.
Step 1 : Write the binary number.
Step 2 : Write the weights $2^{0},2^{1},2^{2},2^{3}$ ,… under the binary digits starting from extreme right.
Step 3 : Cross out any weight under a zero, that is, weight under zeros in the binary number should be deleted.
Step 4 : Add the remaining weights.

Binary Addition : In binary number system there are only 2 digits, that is, 0 and 1. In decimal system we carry 1 for every 10 whereas in binary system we carry 1 for every 2. Hence, rules of addition are as under.

0+0=0
0+1=1
1+0=1
1+1=10

## Latest Jobs

1. Type
Job
Indian Institute of Technology Hyderabad Recruitment of 152 JE, Engineer, Library Assistant, MTS - Last Date 17-02-2020
Location
Date Posted
6 Feb 2020
2. Type
Job
SBI Recruitment of 100 Specialist Officers - Last Date 12-02-2020
Location
Anywhere
Date Posted
4 Feb 2020
3. Type
Job
INDIAN Bank Recruitment 138 Specialist Officers - Last Date - 10-02-2020
Location
Anywhere
Date Posted
3 Feb 2020
4. Type
Job
KVIC Recruitment of 108 Group-B and Group-C categories - Last Date 19-01-2020
Location
MumbaiMaharashtra, India
Date Posted
7 Jan 2020
5. Type
Job
SAIL Durgapur Steel Plant Recruitment of Manager, Technician, Medical Service Provider - 27-01-2020
Location
DurgapurWest Bengal, India
Date Posted
7 Jan 2020
6. Type
Job
Indian Coast Guard Recruitment 260 Navik - Last Date 02-02-2020
Location
Anywhere
Date Posted
7 Jan 2020
7. Type
Job
IOCL hiring 312 Apprentices - Last Date 22-01-2020
Location
Anywhere
Date Posted
7 Jan 2020
8. Type
Job
RBI Recruitment NEWS for 926 Assistants - Last Date 16-01-2020
Location
Anywhere
Date Posted
7 Jan 2020
9. Type
Job
Janki Devi Memorial College Recruitment 71 Assistant Professor - Last Date 04-01-2020
Location
DelhiDelhi, India
Date Posted
2 Jan 2020
10. Type