## Data Types

**Definition**:

Data itself has no meaning, when it is assigned a meaning then it becomes an information. Information is a collection of facts or data. Data is nothing but factual information used for analysis or reasoning. As we all know that the information in computers is Stored in memory or processor registers, Registers contain either data or control information. Binary coded information that are operated on to achieve required computational results is data.

Data types in Registers of digital computers may be classified as-

• Numbers used in arithmetic computations

• Letters of the alphabet used in data processing

• Other discrete symbols used for specific purpose.

Number Systems:

1) Decimal number system

2) Binary number system

3) Octal number system

4) Hexa decimal number system

1.**Decimal number system:**

Decimal numbers means the numbers from 0 to 9 i.e; 10 numbers. So, the radix will become 10. Radix is to determine the quantity that the number represents, it is necessary to multiply each digit by an integer power of ‘r’ and then form the sum of all weighted digits.

Ex:- 2018(10)=(2*103)+(0*102)+(1*101)+(8*100)

2. **Binary number system:**

In digital computers binary numbers are 0 & 1 i.e; there exist only two binary numbers. So the radix will become 2. As it includes only 0’s & 1’s, the example of this number system is as follows

11011001(2)=(1*27)+(1*26)+(0*25)+(1*24)+(1*23)+(0*22)+(0*21)+(1*20)

=217(10)

3. **Octal number system:**

We all know that octal means 8. So the numbers system will take the values from 0 to 7 i.e; 8 also refer as 23. So the radix is 3.

Ex: 346= (3*82)+(4*81)+(6*80)

=192+32+6

=230

4. **Hexadecimal number system:**

Hexadecimal, in this hexa means 6 and decimal means 10. So hexadecimal refers to 16 numbers i.e; 0 to 15 but in case of digital computers numbers exist up to 9 so that, we take 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,&F. The last six symbols are unfortunately identical to the letters do the alphabet & can cause confusion at times. When used to represent hexadecimal digits the symbols A,B,C,D,E,F correspond to the decimal numbers 10,11,12,13,14,15 respectively. The redix will become 16.

Ex: F5= (F*161) + (5*160)

= (15*16) + (5*1) => 240 + 5 = 245

Note: Conversions from and to binary, Octal & hexa decimal, decimal representation plays an important part in digital computers.

Representations:

1. BCD-Binary Coded Decimal

0-0000

1-0001

2-0010

3-0011

4-0100

5-0101

6-0110

7-0111

8-1000

9-1001

2. BCO-Binary Coded Octal

0-000

1-001

2-010

3-011

4-100

5-101

6-110

7-111

3. BCH-Binary Coded Hexadecimal

0-0000

1-0001

2-0010

3-0011

4-0100

5-0101

6-0110

7-0111

8-1000

9-1001

10-A-1010

11-B-1011

12-C-1100

13-D-1101

14-E-1110

15-F-1111

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