DATA REPRESENTATION, BINARY SYSTEM, BIT, BYTE, ASCII CODEChapter 3

Mr.M

oh

am

me

d R

ah

ma

th

DATA REPRESENTATION

• Data Representation refers to the methods used internally to represent information stored in a computer. Computers store lots of different types of information:

• numbers • text • graphics of many varieties (stills, video,

animation) • sound

Mr.M

oh

am

me

d R

ah

ma

th

MEMORY STRUCTURE IN COMPUTER

• Memory consists of bits (0 or 1) – a single bit can represent two pieces of

information • bytes (=8 bits)

– a single byte can represent 256 = 2x2x2x2x2x2x2x2 = 28 pieces of information

• words (=2,4, or 8 bytes) – a 2 byte word can represent 2562 pieces of

information (approximately 65 thousand). • Byte addressable - each byte has its own

address.

Mr.M

oh

am

me

d R

ah

ma

th

BINARY SYSTEM binary numeral system, or base-2 numeral

system, represents numeric values using two symbols: 0 and 1. More specifically, the usual base -2 system is a positional notation with a radix of 2. Numbers represented in this system are commonly called binary numbers.

Bits: A bit (short for binary digit) is the smallest unit of data in a computer. A bit has a single binary value, either 0 or 1.

Byte: a byte is a unit of data that is eight binary digits long. A byte is the unit most computers use to represent a character such as a letter, number, or typographic symbol (for example, "g", "5", or "?").

Mr.M

oh

am

me

d R

ah

ma

th

ASCII CODE

Mr.M

oh

am

me

d R

ah

ma

th

Binary (2) Decimal (10) Octal (8)Hexadecimal

(16)0000' 0 000' 0000'0001' 1 001' 0001'0010' 2 010' 0010'0011' 3 011' 0011'0100' 4 100' 0100'0101' 5 101' 0101'0110' 6 110' 0110'0111' 7 111' 0111'1000' 8   1000'1001' 9   1001'1010' 10   A1011' 11   B1100' 12   C1101' 13   D1110' 14   E1111' 15   F

BINARY TO DECIMAL CONVERSION

Mr.M

oh

am

me

d R

ah

ma

th

1 1 1 0 1 0 1

26 25 24 23 22 21 20

2x2x2x2x2x2

2x2x2x2x2

2x2x2x2

2x2x2

2x2 (a)1= 2

(a)0= 1

64 32 16 8 4 2 1

64x1 32x1 16x1 8x0 4x1 2x0 1x1

64 + 32 +

16 +

0 +

4 +

0 + 1

Q1 ) Convert (1110101)2 =( )10

= (117)10

CLASS WORK

Convert Binary to Decimal1. (101101010)2 = ( )10

2. (100001001)2 = ( )10

3. (111000101)2 = ( )10

4. (101111000)2 = ( )10

5. (010100011)2 = ( )10

6. (101111111)2 = ( )10

Mr.M

oh

am

me

d R

ah

ma

th

DECIMAL TO BINARY CONVERSION

• Q ) (35)10 = ( )2

= (100011)2

Mr.M

oh

am

me

d R

ah

ma

th

CLASS WORK

Convert Decimal to Binary1. (421) 10 = ( ) 2

2. (1025)10 = ( ) 2

3. (368)10 = ( ) 2

4. (687)10 = ( ) 2

5. (625)10 = ( ) 2

6. (752)10 = ( ) 2

Mr.M

oh

am

me

d R

ah

ma

th

BINARY TO HEXADECIMAL

Q ) (101011101010)2 = ( )16

=( AEA)16

Mr.M

oh

am

me

d R

ah

ma

th

1010 1110 1010A E A

CLASS WORK

Convert Binary to Hexadecimal1. (10110101001011100010)2 = ( )16

2. (10000100110110000101)2 = ( )16

3. (11100010101010011010)2 = ( )16

4. (10111100011011101101)2 = ( )16

5. (0101000110110101010)2 = ( )16

6. (101111111010011010)2 = ( )16

Mr.M

oh

am

me

d R

ah

ma

th

HEXADECIMAL TO BINARY

• Q ) (A19)16 = ( )2

=(101000011001)2

Mr.M

oh

am

me

d R

ah

ma

th

A 1 9

1010 0001 1001

CLASS WORK

Convert Hexadecimal to Binary1. (AF1) 16 = ( ) 2

2. (924)16 = ( ) 2

3. (3569)16 = ( ) 2

4. (4526)16 = ( ) 2

5. (6548)16 = ( ) 2

6. (1334)16 = ( ) 2

Mr.M

oh

am

me

d R

ah

ma

th

CHAPTER 3 END

Mr.M

oh

am

me

d R

ah

ma

th