Number System - Formulas, Examples, Shortcuts and Video

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


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.

Basic or Radix :
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.



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