1. Lesson 2 0x
Coding
ASCII Code

2. Number Systems Coding Decimal number system Binary number system
Octal number system
Hexadecimal number system
Conversion
ASCII Code

3. Coding Computer Keyboard Screen Scanner Decoding Coding Printer Mouse
Microphone
All Information are converted into codes to be processed by the computer.
The codes are numbers in the Binary System (1s & 0s)
Why Binary ?
ASCII Code

4. Decimal Number System
This is the used number system in our life calculations.
It contains 10 symbols to represent the numbers which are {0,1,2,3,4,5,6,7,8,9}, any number in the system can be represented in away that it depends on the power of 10.
ASCII Code

5. Decimal (base 10) Examples: 2434=2000+400+30+4
=2x x x10 + 4x1
=2x x102 +3x x100
Example 2:
1479 = 1 * * * * 100
ASCII Code

6. Binary Number system
This number system contains only two symbols to represent its numbers, which are {0 and 1} only.
e.g.: 100, are accepted numbers in the binary system where is not accepted because it contains the symbol (2) which is not included in the set of symbols.
In order to distinguish the numbers in the binary system from the decimal system, they are put in parenthesis and the number 2 is put to the bottom right of the brackets as a subscript; like (1001)2 for the binary system , and the number 10 is put to for the decimal system ; like (1001)10.
ASCII Code

7. Conversion from Binary to Decimal1 1 1
Example: (1101) 2 = 8x1 + 4x1 + 2x0 +1x1 = (13) 10 1
(100)2= 1x22 + 0x21 + 0x 20
=1x4 + 0x2 + 0x1
= = (4)10
ASCII Code

8. Conversion from Binary to Decimal1 1 1
(1011)2=1x23 + 0x22 + 1x x 20
=1x 8 + 0x4 + 1 x x 1
= =(11)10
Exercise: What are the decimal values for the following binary numbers:
a- (10010)2 b- ( )2 c- ( )2
ASCII Code

9. Conversion from Binary to Decimal
Rule: If the binary number consists of only ones, you can find its decimal equivalent number using this formula: Decimal = 2n – 1 Where n is the number of bits, for example 1111 has 4 bits.
Example 1:
( )2 has 8 bits, so
Decimal = 28 – 1 = 255
Example 2:
( )2 has 9 bits, so
Decimal = 29 – 1 = 511
Binary
Decimal 1 11 3
111 7
1111 15
11111 31
111111 63
127
255
511
1023
2024
ASCII Code

10. Conversion from Binary to Decimal fraction
2-1
2-2
2-3
2-4
0.5
0.25
0.125
0.0625
Examples
Convert binary to decimal:
1) 2)
( )2
( )2
Sol. Sol.
= = (6.125) =
=(46.625)10
ASCII Code

11. Decimal to binary conversion
Example: 43
43 ÷ 2: Quotient 21, remainder 1: Result > 1
21 ÷ 2: Quotient 10, remainder 1: Result > 1 1
10 ÷ 2: Quotient 5, remainder 0: Result > 0 1 1
5 ÷ 2: Quotient 2, remainder 1: Result >
2 ÷ 2: Quotient 1, remainder 0: Result >
1 ÷ 2: Quotient 0, remainder 1: Result >
Exercise: Convert the following decimal numbers to binary 22 63
174
3000
ASCII Code

12. Decimal to binary conversion8
1000 16
10000 1 9
1001 17
10001 2 10
1010 18
10010 3 11
1011 19
10011 4
100 12
1100 20
10100 5
101 13
1101 21
10101 6
110 14
1110 22
10110 7
111 15
1111 :
ASCII Code

13. Fractions conversion from decimal to binary
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14. Fractions conversion from decimal to binary
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15. Count…
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16. Count… Exercise: convert the following decimal numbers to binary:
a- (85) b- (117) c- (43.75) d- ( ) e- (36.045)
2- Arrange the following binary numbers in ascending order
a b c d
ASCII Code

17. Octal Number system
This system contains 8 digits (symbols) which are the first 8 decimal digits (0,1,2,3,4,5,6,7); (there are no 8 & 9 in the octal number system). Valid numbers in octal system: Invalid numbers in octal system: Numbers are presented in this systems in parentheses with subscript 8 to separate them among other number system e.g. (45612)8
ASCII Code

18. Octal Number (base 8) Example: convert (3057)8 to decimal.
Sol =3x83+0x82+5x81+7x80
=3x512+0x64+5x8+7x1 =
=1583
then (3057)8 is equivalent to (1583)10
ASCII Code

19. Decimal to octal conversion
Example 1: (173)8
Sol. Remainder
21 8 5
2 8 2
The result is ( 25 5)8
ASCII Code

20. Example 2: (1583)10 Sol. Remainder 1583. 8. 197. 8. 7. 24. 8. 5. 3. 8
Example 2: (1583)10 Sol. Remainder The result is ( 3057)8
Example 2: (1583)10 Sol. Remainder The result is ( 3057)8
ASCII Code

21. Converting decimal fractions to octal
This can be obtained by multiply the decimal fraction by 8 and watch the carry into integer’s position. Example: (0.23) x 8 = x 8 = x 8 = ∴ (0.23)10 ≡ (0.165)8
ASCII Code

22. Octal to binary conversion
Because 8 = 23 , we can convert from octal to binary directly, that is each digit in octal will match 3 digits in binary as follows:
ASCII Code

23. CONT…
ASCII Code

24. Binary to octal conversion
Binary to octal conversion: this conversion can be obtained as an opposite to the conversion from octal to binary that is grouping the binary number into threes, and converting them to octal ones.
Examples: convert from binary to octal.
Answer:
∴( )2≡ (715)8
ASCII Code

25. Hexadecimal Number system
This system contains sixteen symbols to represent its numbers, Which are:
{0,1, 2, 3 ,4,5,6,7,8,9,A,B,C,D,E,F}
Where
A represent the value (10)10,
B represent (11)10,
C represent (12)10,
D represent (13)10,
E represent (14)10,
F represent (15)10.
ASCII Code

26. Cont….
Valid numbers in hexadecimal numbers: 78A 100 A4BB To distinguish hexadecimal number from other systems, we put the hexadecimal numbers between two parenthesis like (49B3)16. The weights of the numbers in hexadecimal number system are evaluated according to the positional number system:
ASCII Code

27. Converting from hexadecimal to decimal:
Examples: (34)16 Solution: 3x x160 =3x16 + 4x1 =48+4 =(52)10 (34)16  (52)10 (40AC)16 Solution: 4 x x Ax161 + Cx160 =4 x x x x 1 = =(16556)10 (40AC)16  (16556)10
ASCII Code

28. Converting from decimal to hexadecimal:
ASCII Code

29. Converting from hexadecimal to Binary:
because 16=24 then a hexadecimal number can be converted directly to 4 binary digits ass follows:

30. Converting from hexadecimal to Binary:
ASCII Code

31. Converting from Binary to hexadecimal:
we group each 4 numbers to convert them into one hexadecimal number.
ASCII Code

32. Conversion Diagram Octal(8) Decimal(10) Binary(2) Hex(16)
by the Base and take the reminder
Use the table directly
Decimal(10)
Binary(2)
By the Weight and take the Sum
Hex(16)
ASCII Code

33. ASCII Code
ASCII stands for American Standard Code for Information Interchange.
The ASCII is a 7 bits code whose format is X6X5X4X3X2X1X0, where each X is 0 or 1.
The ASCII code is used to represent the English language characters (letters, numbers, symbols and punctuations) by binary numbers to used in computers.
ASCII Code

34. Cont.... ASCII Code
Notes:
In computer processing the “space” is a significant character, where the ASCII code of the space is
Upper case and lower case letters have different values in ASCII code.
For example the ASCII code for A is and the ASCII code for a is
ASCII Code

35. Ascii Code
ASCII Code

36. Write Print S in ASCII code.
Example:
Write Print S in ASCII code.
P( ) r( ) i( ) n( ) t( ) space( ) S( )
ASCII Code

37. Parity Bit
Note: Read page number 122 from the book.
The parity bit is an additional bit added to the ASCII code to catch errors in transmitting data.
So, the message format for each character (ASCII code with parity bit) is X7X6X5X4X3X2X1X0
ASCII
Parity ِbit
ASCII Code

38. Types of Parity Bit:
Odd Parity Bit: in this type number of ones in the message for each character (ASCII code and parity bit) must be odd.
Even Parity Bit: in this type number of ones in the message for each character (ASCII code and parity bit) must be even.
ASCII Code

39. Suppose that two devices are communicating with even parity.
The transmitting device (Sender) sends data, it counts the number of ones in each group of seven bits. If number of ones is even, it sets the parity bit to 0; if the number of ones is odd, it sets the parity bit to 1.
In this way, every message has an even number of ones.
ASCII Code

40. Cont... Parity Bit
On the receiving side, the device checks each message to make sure that it has an even number of ones.
If the receiving device finds an odd number of ones, the receiver knows there was an error during transmission.
ASCII Code

41. Binary Coded Decimal(BCD):
a format for representing decimal numbers (integers) in which each digit is represented by four bits . For example, the number 375 would be represented as:
ASCII Code