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ASCII Code1
Coding
Lesson 2 0x002
010
Number Systems
• Coding • Decimal number system• Binary number system• Octal number system• Hexadecimal number system• Conversion
ASCII Code2
Coding
ASCII Code3
Keyboard
Computer Screen
Printer
Scanner
Mouse
Microphone
Coding Decoding
All Information are converted into codes to be processed by the computer.The codes are numbers in the Binary System (1s & 0s)Why Binary ?
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 Code4
Decimal (base 10)
Examples: 2434=2000+400+30+4 =2x1000 + 4x100 + 3x10 +
4x1 =2x103 + 4x102 +3x101 + 4x100
Example 2:
1479 = 1 * 103 + 4 * 102 + 7 * 101 + 9 * 100
ASCII Code5
Binary Number system
• This number system contains only two symbols to represent its numbers, which are {0 and 1} only.
• e.g.: 100, 101 1000001010 are accepted numbers in the binary system where 10020 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 Code6
Conversion from Binary to Decimal
ASCII Code7
Example: (1101) 2 = 8x1 + 4x1 + 2x0 +1x1 = (13) 10
111 0
• (100)2= 1x22 + 0x21 + 0x 20
=1x4 + 0x2 + 0x1 =4 + 0 +0= (4)10
001
Conversion from Binary to Decimal
• Exercise: What are the decimal values for the following binary numbers:
a- (10010)2 b- (1110111)2 c- (1011011)2
ASCII Code8
(1011)2=1x23 + 0x22 + 1x 21 + 1x 20
=1x 8 + 0x4 + 1 x 2 + 1 x 1 = 8 + 0 +2 +1=(11)10
111 0
Conversion from Binary to Decimal
ASCII Code9
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.
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 :(11111111)2 has 8 bits, so
Decimal = 28 – 1 = 255
Example 2: (111111111)2 has 9 bits, so
Decimal = 29 – 1 = 511
Binary Decimal1 111 3111 71111 1511111 31111111 631111111 12711111111 255111111111 5111111111111 102311111111111 2024
Conversion from Binary to Decimalfraction
ASCII Code10
2-1 2-2 2-3 2-4
0.5 0.25 0.125 0.0625
ExamplesConvert binary to decimal: 1) 2)
(110.001)2
(101110.101)2
Sol. Sol.1 1 0 . 0 0 11 0 1 1 1 0 . 1 0 1
4 2 1. . 5. 25. 125 32 16 8 4 2 1. . 5. 25. 125
4 2 1 . .5 .25. 12532 16 8 4 2 1. . 5 .25 .125
=4+ 2. + 125) = 6.125(10 =32 + 8 + 4+ 2. + 5. + 125
=(46.625)10
Decimal to binary conversion
ASCII Code11
Example: 4343 ÷ 2 :Quotient 21, remainder 1: Result > 1
21 ÷ 2 :Quotient 10, remainder 1: Result > 1 110 ÷ 2 :Quotient 5, remainder 0: Result > 0 1 1
5 ÷ 2 :Quotient 2, remainder 1: Result > 1 0 1 12 ÷ 2 :Quotient 1, remainder 0: Result > 0 1 0 1 11 ÷ 2 :Quotient 0, remainder 1: Result > 1 0 1 0 1
1• Exercise: Convert the following decimal numbers to binary22631743000
ASCII Code12
Decimal Binary Decimal Binary Decimal Binary
0 0 8 1000 16 10000
1 1 9 1001 17 10001
2 10 10 1010 18 10010
3 11 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 : :
Decimal to binary conversion
Fractions conversion from decimal to binary
ASCII Code13
Fractions conversion from decimal to binary
ASCII Code14
Count…
ASCII Code15
Count…
ASCII Code16
Exercise: convert the following decimal numbers to binary:
a- (85) b- (117) c- (43.75) d- (0.15625) e- (36.045)
2- Arrange the following binary numbers in ascending order a- 1101 b- 1110 c- 1011.11 d- 1101.001
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: 45612 70125 20 10001Invalid numbers in octal system: 455801 94 8000Numbers are presented in this systems in parentheses with subscript 8 to separate them among other number system e.g. (45612)8
ASCII Code17
Octal Number (base 8)
• Example: convert (3057)8 to decimal.
• Sol. 3057=3x83+0x82+5x81+7x80
• =3x512+0x64+5x8+7x1• =1536+0+40+7• =1583• then (3057)8 is equivalent to
(1583)10 ASCII Code18
Decimal to octal conversion
• Example 1: (173)8
• Sol. Remainder• 173 8 5• 21 8 5• 2 8 2• The result is ( 25 5)8
ASCII Code19
Example 2: (1583)10
Sol. Remainder 15838
19787248538003
The result is ( 3057)8
Example 2: (1583)10
Sol. Remainder 1583 8
1978 7248 538 00 3
The result is ( 3057)8
ASCII Code20
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)10
0.23 x 8 =1.84 10.84 x 8 = 6.72 60.72 x 8 = 5.76 5
∴ (0.23)10 ≡ (0.165)8
ASCII Code21
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 Code22
ASCII Code23
CONT…
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: 111001101 111 001 101• • •
7 1 5• ∴(111 001 101)2≡ (715)8
ASCII Code24
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 Code25
Cont….
Valid numbers in hexadecimal numbers:78A 100 A4BBTo 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 Code26
Converting from hexadecimal to decimal:
Examples:(34)16
Solution: 3x161 + 4x160
=3x16 + 4x1=48+4 =(52)10 (34)16 (52)10
(40AC)16
Solution: 4 x 163 + 0 x 162 + Ax161 + Cx160
=4 x 4096 + 0 x 265 + 10 x 16 + 12 x 1=16384 + 0 + 160 + 12=(16556)10 (40AC)16 (16556)10
ASCII Code27
Converting from decimal to hexadecimal:
ASCII Code28
Converting from hexadecimal to Binary: • because 16=24 then a hexadecimal number
can be converted directly to 4 binary digits ass follows:
29
ASCII Code30
Converting from hexadecimal to Binary:
Converting from Binary to hexadecimal: • we group each 4 numbers to
convert them into one hexadecimal number.
ASCII Code31
ASCII Code32
Decimal(10)
Octal(8)
Binary(2)
Hex(16)
by the Base and take the reminder
By the Weight and take the Sum
Use the table directly
Conversion Diagram
ASCII Code33
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 Code34
Cont.... ASCII Code
Notes:In computer processing the “space” is a
significant character, where the ASCII code of the space is 0100000 .
Upper case and lower case letters have different values in ASCII code.
For example the ASCII code for A is 1000001 and the ASCII code for a is 1100001.
Ascii Code
ASCII Code35
ASCII Code36
Example:
Write Print S in ASCII code.
P(101 0000) r(111 0010) i(110 1001) n(110 1110) t(111 0100) space(010 0000) S(101 0011)
ASCII Code37
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
ASCIIParity 4bit
ASCII Code38
Types of Parity Bit:1. Odd Parity Bit: in this type
number of ones in the message for each character (ASCII code and parity bit) must be odd.
2. Even Parity Bit: in this type number of ones in the message for each character (ASCII code and parity bit) must be even.
ASCII Code39
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 Code40
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.
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 Code41