What Is Number System - Computer Fundamental
Category: COMPUTER SCIENCE | 14th March 2024, Thursday
You Know That Computer Stores And Processes Two Basic Types Of Data Viz.,character And Number. The Character Type Data Includes Alphabets And Some Special Symbols, While The Number Data Type Includes Numerical Data On Which Arithmetic Calculations Can Be Done. For Example, Student Name Contains Character Data, Roll Number Will Have Numeric Data.
Digital Computers Internally Use The Binary (base 2) Number System To Represent Data And Perform Arithmetic Calculations. The Binary Number System Is Very efficient For Computers, But Not For Humans. Representing Even Relatively Small Numbers With The Binary System Requires Working With Long Strings Of Ones And Zeroes.
Binary Numbers
Binary Numbers Are Combination Of Two Basic Numbers (zero And One) While Decimal Numbers Are Combinations Of 0, 1, 2, 3, 4, 5, 6, 7, 8 And 9.All The Numbers Which Are Generated By Decimal Numbers Can Also Be Generated By Binary Numbers. Binary Number Has Base 2 Because All Numbers Are Generated By Combination Of Only Two Numbers ( 0 And 1) And Decimal Number Has Base 10 Because All Numbers Are Generated By Combination Of Only Ten Numbers ( 0 To 9).
Octal Number And Hexadecimal Numbers
Octal (base 8) Was Previously A Popular Choice For Representing Digital Circuit Numbers In A Form That Is More Compact Than Binary. Octal Is Sometimes Abbreviated As Oct. Octal Counting Starts At 0 And Goes: 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13 14 15 And So On.
Hexadecimal (base 16) Is Currently The Most Popular Choice For Representing Digital Circuit Numbers In A Form That Is More Compact Than Binary. Hexadecimal Numbers Are Sometimes Represented By Preceding The Value With ‘0x’, As In
0x1B84. Hexadecimal Is Sometimes Abbreviated As Hex. Hexadecimal Counting Goes: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, And So On.
The Following Table Shows The Decimal Number 0 To 15 And Its Corresponding Binary, Octal And Hexadecimal Values.
Decimal, Binary, Octal And Hexadecimal Values
| Decimal | Binary | Octal | Hexadecimal |
| 0 | 0000 | 000 | 0 |
| 1 | 0001 | 001 | 1 |
| 2 | 0010 | 002 | 2 |
| 3 | 0011 | 003 | 3 |
| 4 | 0100 | 004 | 4 |
| 5 | 0101 | 005 | 5 |
| 6 | 0110 | 006 | 6 |
| 7 | 0111 | 007 | 7 |
| 8 | 1000 | 010 | 8 |
| 9 | 1001 | 011 | 9 |
| 10 | 1010 | 012 | A |
| 11 | 1011 | 013 | B |
| 12 | 1100 | 014 | C |
| 13 | 1101 | 015 | D |
| 14 | 1110 | 016 | E |
| 15 | 1111 | 017 | F |
All Four Number Systems Are Equally Capable Of Representing Any Number. Furthermore, A Number Can Be Perfectly Converted Between The Various Number Systems Without Any Loss Of Numeric Value.
Conversion From One System To Another
1. Decimal To Binary Conversion
There Are Two Methods You Can Use: Successive Division And Subtracting Values Using A Table. Successive Division Requires Dividing Continuously By The Base We Are Converting To Until The Quotient Equals 0. The Remainders Compose The Answer.
Steps For Conversion From Decimal To Binary
1. Divide The Decimal Number By 2.
2. Take The Remainder And Record It On The Side.
3. Repeat Until The Decimal Number Can Not Be Divided Into Any More.
4. With The Bits, Record Them In Order From Right To Left As That Will Be The Number
in Base 2.
For Example, Convert 9 Into Binary As Follows;
9/2 = 4 And Remainder = 1 First Remainder Is Called LSB (least Significant Bit)
4/2 = 2 And Remainder = 0
2/2 = 1 And Remainder = 0
1/2 = 0 And Remainder = 1 Last Remainder Is Called MSB (Most Significant Bit)
Now, Decimal 9 Is Equivalent To 1001 Binary Number
Decimal To Octal Conversion
We Can Convert Decimal To Octal And Hexadecimal By Using The Similar Conversion Method Of Decimal To Binary. I.e., Successive Division, Which Requires Dividing Continuously By The Base We Are Converting To Until The Quotient Equals 0. The Remainders Compose The Answer.
Steps For Conversion From Decimal To Octal
1. Divide The Decimal Number By 8.
2. Take The Remainder And Record It On The Side.
3. Repeat Until The Decimal Number Can Not Be Divided Any More.
4. With The Bits, Record Them In Order From Right To Left As That Will Be The Number In Base 8.
For Example, To Convert 19 Into Octal Follow The Steps:
19/8=2 And Remainder = 3 First Remainder Is Called LSB (least Significant Bit)
2/8=0 And Remainder = 2 Last Remainder Is Called MSB (Most Significant Bit)
Now Decimal Number 19 Is Equivalent To Octal Number 23 (19)10= (23)8
Decimal To Hexadecimal Conversion
Division Method Can Be Used For Conversion From Decimal To Hexadecimal.
Steps For Conversion From Decimal To Hexadecimal
1. Divide The Decimal Number By 16
2. Take The Remainder And Record It On The Side.
3. Repeat Until The Decimal Number Can Not Be Divided Into Any More.
4. With The Bits, Record Them In Order From Right To Left As That Will Be The Number In Base 16.
For Example, To Convert Decimal Number 229 Into Hexadecimal Number:
229/16 = 14 And Remainder = 5 First Remainder Is Called LSB (least Significant Bit)
14/16 = 0 And Remainder = 14 Last Remainder Is Called MSB (Most Significant Bit)
In Hexadecimal 10,11,12,13,14,15 Are Equivalent To A,B,C,D,E,F Respectively
So (229)10= (E5)16
Binary To Decimal
To Find The Decimal Representation Of A Binary Number Simply Take The Sum Of Products Of Binary Digits And The Powers Of 2 Which They Represent.
For Example, Conversion Of (1000)2 Into Decimal Is As Follows:
(1000)2 = 1 × 23 + 0 × 22 + 0 × 21 + 0 ×20
= 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1
(1000)2 = 8 + 0 + 0 + 0 = 8
Octal To Decimal
To Find The Decimal Representation Of An Octal Number Simply Take The Sum Of Products Of Octal Digits And The Powers Of 8 Which They Represent.
For Example,
Conversion Of (1000)8 Into Decimal Is As Follows:
(1000)8 = 1 × 83 + 0 × 82 + 0 × 81 + 0 ×80
= 1 × 512 + 0 ×64 + 0 × 8 + 0 × 1
(1000)8 = 512 + 0 + 0 + 0 = 512
Hexadecimal To Decimal
To Find The Decimal Representation Of A Hexadecimal Number Simply Take The Sum Of Products Of Hex Number And The Powers Of 16 Which They Represent.
For Example,
Conversion Of (1000)16 Into Decimal Is As Follows:
(1000)16 = 1 × 163 + 0 × 162 + 0 × 161 + 0 ×160
= 1 × 4096 + 0 ×256 + 0 × 16 + 0 × 1
(1000)8 = 4096 + 0 + 0 + 0 = 4096
Now Let Us Learn About One’s Complement And Two’s Complement Of A Binary Number.
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Number System, What Is Number System
