Data representation in computers

DATA REPRESENTATION IN

COMPUTERS

BINARY REPRESENTATION

OF DATA

•Bit - a fundamental unit of

information having just two

possible values, as either of the

binary digits 0 or 1.

•Byte - a unit of digital information

in computing and

telecommunications that most

commonly consists of eight bits.

DIGITAL REPRESENTATION•Within a computer, information is

represented and stored in a

digital binary format.

• The term bit is an abbreviation of

binary digit and represents the

smallest piece of data.

• Humans interpret words and

pictures; computers interpret

only patterns of bits.

NUMBERING SYSTEMS

•Number System Base Symbols used

• Binary 2 0,1

•Octal 8 0,1,2,3,4,5,6,7

•Decimal 10 0,1,2,3,4,5,6,7,8,9

•Hexadecimal 16

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

where A = 10; B = 11; C = 12; D =

13;

USING POSITIONAL NOTATION

USING DOUBLING

Use this method to convert

from any base to decimal. Doubling is

used because the given number is of

base 2. If the given number is of a

different base, replace the 2 in the

method with the base of the given

number. For example, if the given number

is in base 37, you would replace the "x 2"

with "x 37". The final result will always be in decimal (base 10).

PRACTICE

1. 110100012

2. 110012

3. 111100012

CONVERT DECIMAL NUMBERS TO BINARY

• Example:

25

25/2

12/2

6/2

3/2

1/2

25 = 11001

Quotien

t

12

6

3

1

0

Remaind

er

1

0

0

1

1

CONVERT DECIMAL NUMBERS TO BINARY

Checking:

1 1 0 0 1 multiplier

16 8 4 2 1 equivalents

16 8 0 0 1 results16+8+0+0+1 = 25

•Direction: Convert the decimal

numbers shown below to binary.

Perform checking to verify

answers.

1) 19

2) 28

3) 37