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University of Palestine Faculty of Engineering and Urban planning Software Engineering Department. Digital Logic Design ESGD2201. Lecture 2. Number Systems. Eng. Mohammed Timraz Electronics & Communication Engineer. Wednesday, 10 th September 2008. Agenda. 1. Decimal Number

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slide1

University of Palestine

Faculty of Engineering and Urban planning

Software Engineering Department

Digital Logic Design ESGD2201

Lecture 2

Number Systems

Eng. Mohammed Timraz

Electronics & Communication Engineer

Wednesday, 10th September 2008

slide2

Agenda

1. Decimal Number

2. Binary Numbers

2.1 Binary to Decimal Conversion

2.2 Decimal to Binary Conversion

3. Octal Numbers

3.1 Octal to Decimal Conversion

3.2 Decimal to Octal Conversion

3.3 Binary to Octal Conversion

3.4 Octal to Binary Conversion

4. Hexa Decimal Numbers

4.1 Binary to Hexa Decimal Conversion

4.2 Hexa Decimal to Binary Conversion

4.3 Hexa Decimal to Decimal Conversion

4.4 Decimal to Hexa Decimal Conversion

slide3

Number Systems

1- Decimal Number:

[Base10],

*Integer Number:[0,1,2,3,………..9]

Example:-

[23]10=3×100 +2×101

=3×1+2×10

=3+20= 23

slide4

Number Systems

Decimal Number

*Float Number:

[16.15]

Integer part float part

Decimal Point

Example:-[16.15]

16.15=6*100+1*101+1*10-1+5*10-2

=6 + 10+ 0.1 + 0.05

=16.15

…..104 103 102 101 . 10-1 10-2 10-3 10-4 …..Decimal Point

slide5

Number Systems

2. Binary Numbers:

[Base 2],[ 0,1]

ex:- 00 ,01 ,10 ,11

Decimal Binary

slide6

Number Systems

2-1 Binary to Decimal Conversion:

Example:- [1101101]2

1 1 0 1 1 0 1

MSB LSB

Most significant BIT Least Significant Bit

slide7

Number Systems

2-1 Binary to Decimal Conversion:

Example:-

For integer numbers,

[1101101]2 = [ ? ]10

1 1 0 1 1 0 1

26 25 24 23 22 21 20

[1101101]2 =1×20+0×21+1×22+1×23+0×24+1×25+1×26

=[109]10

MSB LSB

slide8

Number Systems

2-1 Binary to Decimal Conversion:

Example:-

For float numbers,

[10.111]2 = [ ? ]10

1 0 . 1 1 1

21 20 2-1 2-2 2-3

[10.111]2 =0×20+1×21+1×2-1+1×2-2+1×2-3

=[2.875]10

Note: MSB & LSB just for integer part.

Binary

point

slide9

Number Systems

Number Systems

2-1 Binary to Decimal Conversion:

Example:-

[1011]2 = [ ? ]10

1 0 1 1

23 22 21 20

[1011]2 =1×20+1×21+0×22+1×23

=[11]10

slide10

Number Systems

Number Systems

  • 2-2 Decimal to Binary Conversion:
  • There are two ways to convert the decimal numbers to binary numbers.
  • By using the Truth Table: we can use the truth table for small decimal numbers, but for large decimal numbers it will be more difficult.
  • So, we will use the division: which we can use it for small and large decimal numbers
slide11

Number SystemsThe Truth Table

Decimal to Binary

Conversion:

slide12

Number Systems

Number Systems

Decimal to Binary Conversion:

The Division:

[198]10 = [ ? ]2

By using the division system:

Carrier

0

1

1

0

0

0

1

1

1

1

0

1

1

0

0

0

slide13

Number Systems

Number Systems

Decimal to Binary Conversion:

The Division:

For float numbers,

[0.3125]10 = [ ? ]2

By using

the multiplication system:

MSB LSB

. 0

0

1

1

Carrier

0

0.3125 × 2 = 0.625

1

0.625 × 2 = 1.25

0

1.25 × 2 = 0.5

0.5 × 2 = 1.00

1

Continuo to the desired number of decimal places or stop when fractional part is all zero

slide14

Number Systems

3. Octal Numbers:

[Base 8],[ 0,1,3,4,5,6,7]

3-1 Octal to Decimal Conversion:

Example:-

[2374]8 = [ ? ]10

=4×80+7×81+3×82+2×83

=[1276]10

slide15

Number Systems

Number Systems

3-2 Decimal to Octal Conversion:

The Division:

[359]10 = [ ? ]8

By using the division system:

Carrier

7

4

5

4

7

5

slide16

Number Systems

3-3 Binary to Octal Conversion:

Example:-

[110101]2 = [ ? ]8

Here we will take 3 bits and convert it from binary to decimal by using the decimal to binary truth table:

BinaryDecimal

1 1 0 1 0 1 = (65)8

{

{

6

5

slide17

Number Systems

3-4 Octal to Binary Conversion:

Example:-

[13]8 = [ ? ]2

Here we will convert each decimal digit from decimal to binary (3 bits) using the decimal to binary truth table:

BinaryDecimal

(13)8 = (001011)2

slide18

Number Systems

4. Hexa Decimal Numbers:

[Base 16],[ 0,1,3,4,5,6,7,8,9,A,B,C,D,E,F]

4-1 Binary to Hexa Decimal Conversion:

Example:-

[1100101001010111]2 = [ ? ]16

Here we will take 4 bits and convert it from binary to decimal by using the decimal to binary truth table:

1100 1010 0101 0111

{

{

{

{

C

A

5

7

Then, [1100101001010111]2 = [CA57]16

slide19

1101

1110

0010

0111

Number Systems

4-2 Hexa Decimal to Binary Conversion:

Example:-

[DE27]16 = [ ? ]2

Here we will convert each Hexa decimal digit from decimal to binary (4 bits) using the decimal to binary truth table:

D

E

2

7

Then, [DE27]16 = [1101111000100111]2

slide20

Number Systems

4-3 Hexa Decimal to Decimal Conversion:

Example:-

[B2F8]16 = [ ? ]10

=8×160+F×161+2×162+B×163

=[45816]10

Where, B=11, and F=15

slide21

Number Systems

4-4 Decimal to Hexa Decimal Conversion:

Example:-

[650]10 = [ ? ]16

By using the division system:

Carrier

10

8

2

8

A

2

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