What is Number system

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Number system

  1. Representation of a digit or number in different ways is called number system.
  • A number system defines a set of values used to represent quantity.

Information Representation and codes

  • Humans commonly use decimal number systems consisting of 0,1,2,3–9 but in computer instruction as well as data storing in binary number (0,1) system consisting of a string of 0,s and 1,s (001011101000110101).

The computer is required to store the following type of data

  1. The number used in arithmetic computation.
  2. Alphabets are used in symbolic instructions.
  3. Special character or symbol like #,*,&,%,@,$,|,\ etc.
  4. computer internally sere all the data in binary(0,1)forms (string of 0,s & 1,s) but since binary (0,1) numbers are awful (very hard) to see and work with.

i.e. octal and hexadecimal numbers are now widely used to compress long strings of binary data.

Following numbers system in which data represented

  1. BINARY NUMBER SYSTEM
  2. OCTAL NUMBER SYSTEM
  3. HEXADECIMAL
  4. BINARY CODED DECIMAL (BCD)

MSD (Most Significant Digit):-

The leftmost digit having the highest weight is called as the most significant digit of a number

EX:- (2436)10 Where 2 is Most Significant Digit

LSD (Least Significant Digit):-

The rightmost digit having the lowest weight is called as the least Significant Digit of a number.

EX:-(124225)10 Where 5 is Least Significant Digit.

Types of Number system

There are four types of number system.

NO.SYSTEMDIGITBASE/RADIS
1. BINARY0 & 12
2. OCTAL0 TO 78
3. DECIMALO TO 910
4. HEXADECIMAL0 TO F
A-10,B-11,C-13,D-14,E-15,F-16		16

Radix or Base:-

  • The number of values that a digit can assume is equal to the base of the system.

EX:-A decimal no contains 10 digits.

i.e. 0,1,2,3—9, So its base or radix is 10.

  • The largest value of a digit is always one less than the Base.

1. Binary Number system

  • A Number system in which only two digits present are 0,1 and its base is 2 is called a Binary number system.

EX:-(100111)2 , (000101010.010101)2 Where point is is Binary point

2. Octal Number system

  • A Number system in which only eight digits are present they are 0,1,2,3,4,5,6,7 and the base/radix is 8 is called an octal number system.

EX:-(124)8 , (2135.234)8 , (2345)8 Where point is called octal point

3. Decimal Number system

  • A Number system in which only ten-digit present they are 0,1,2,——–9 and the base /radix is 10 is called a Decimal number system.

EX:-(101)10 , (1248)10 , (15446.1243)10 Where point is called Decimal point

4. Hexadecimal Number system

  • A Number system in which only sixteen digits present are 0,1,2,3—-F is called a Hexadecimal number system.
  • Its base is 16.
  • The values of
  • A=10
  • B=11
  • C=12
  • D=13
  • E=14
  • F=15
  • Hexadecimal number system is also called as alphanumeric number system.

EX:- (C7F3C)16 (36B.014C)16 Where point is called Hexadecimal point

Conversion of Number System

There are following conversion present in numbers system

  • Decimal to Binary
  • Decimal to Octal
  • Decimal to Hexadecimal
  • Binary to Decimal
  • Octal to Decimal
  • Hexadecimal to Decimal
  • Octal to Binary
  • Binary to Octal
  • Binary to Hexadecimal
  • Hexadecimal to Binary
  • Hexadecimal to Octal
  • Octal to Hexadecimal

1.Decimal to Binary:-

  • Step 1: Divide by 2.
  • Step2:-Store Remainders
  • Step 3:- Write the remainder from bottom to Top.

2.Decimal to octal:-

  • Step 1:-Divide by 8.
  • Step 2:-Store Remainders
  • Step 3:- Write the remainder from bottom to Top.

3.Decimal to Hexadecimal

  • Step 1:-Divide by 16.
  • Step 2:-Store Remainders
  • Step 3:- Write the remainders from bottom to Top.

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