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### Chapter 03

Number and Character Coding System

Khan Academy: Number system and conversion

3.1 Denary (Base 10), BInary (Base 2) and Hexadecimal Number (Base 16) systems

 Denary Binary Hexadecimal 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F

3.2 Number System conversion

3.3 Bit, Byte and Word

 Unit Abbr Remarks Bit b Byte B 1B = 8b KiloByte KB 1KB = 210 = 1024B MegaByte MB 1 MB = 1024 KB =  220 B GigaByte GB 1 GB = 1024 MB =  230 B TeraByte TB 1 TB = 1024 GB =  240 B

Transmission Speeds
 Unit Abbr Remarks bit per second bps Kilobits per second kbps 1 kbps = 1000 bps Megabits per second Mbps 1 Mbps = 1000 kbps Gigabits per second Gbps 1 Gbps = 1000 Mbps

Signed and magnitude: The leftmost bit is known as signed bit that specifies the sign of a binary integer.

4 bit representation of integer using different method
 LeftmostMSB rightmostLSB unsigned integer 8 4 2 1 Signed and magnitude 1: negative0: positive 4 2 1 2's complement -8 4 2 1

 Word length Unsigned Integer Signed and magnitude 2's Complement Minimum Maximum Minimum Maximum Minimum Maximum 4-bit 0000(2)= 0 1111(2)= 15 = 24 - 1 1111(2)= -7 0111(2)= 7 1000(2)= -8 0111(2)= +7 8-bit 00000000= 0 11111111=255 = 28 - 1 11111111= -127= - (27 - 1) 01111111= 127=27 - 1 10000000= -128= -27 01111111= 127= 27 - 1 16-bit 0 216 - 1= 65535 - (215 - 1)= - 32767 215 - 1 -215 = -32768 215 - 1 24-bit 0 224 - 1 = 16777215 - (223 - 1) 223 - 1 -223 223 - 1

4-bit
 unsigned signed and magnitude 2's complement 0000 0 0 0 0001 1 1 1 0010 2 2 2 0011 3 3 3 0100 4 4 4 0101 5 5 5 0110 6 6 6 0111 7 7 7 1000 8 0 -8 1001 9 -1 -7 1010 10 -2 -6 1011 11 -3 -5 1100 12 -4 -4 1101 13 -5 -3 1110 14 -6 -2 1111 15 -7 -1

43 = 00101011

-43  sign & mag : 10101011

Express 43 in 2's complement (8 bits)

Method 1:
 For -ve number, the first bit must be 1 (-128) - 43 = -128 + 85Convert 85 into binary (8-1 bits) : 1010101       2's complement: 11010101

Method 2
 Example: The 8-bit representation of -43 using 2's complementStep 1: Convert 43 to binary.   43 = 101011Step 2: Add leading 0 up to 8-bit: 00101011Step 3: Inverted all the bits           11010100  (1's complement)Step 4: Add 1 to the bit pattern:    11010101

Activity 2 on P.89

Class work
Find out the 8-bit representation of -59, -110, -83 using 2's complement, signed and magnitude.

Try out: the 8-bit representation of -130 using 2's complement, signed and magnitude.

Practical 1
Using Google Spreadsheet or excel, tryout the following functions. (P.98-99 of texbook). Share the document to public and submit the hyperlink.
 BIN2DEC BIN2HEX DEC2HEX DEC2BIN HEX2BIN HEX2DEC

After completing the worksheet, please share your google sheet by putting your file in the share folder.

3.4 Addition and subtraction of different number representations

Class work:

2's complement
Addition

Nov 20 (Day 10):
Activities 4 (P.99)
Homework / Classwork:
P.104 - 106 (Do it on an exercise book)  ALL questions except LQ 2a (we do it in class)

Practical on Flash. (chapter 4: multimedia)

Short test on Nov 26 (Day 4) - Test on Chapter 3

3.5 Character coding systems

 Coding Language Length ASCII English 1 Byte GB simplified Chinese 2 Bytes BIg 5 Traditional Chinese 2 Bytes Unicode Multi-language variable length (2, 3, 4 Bytes)

GB, Big 5, Unicode are compatible with ASCII

P.107 Long questions
Q1.

P.103 Self-assessment corner (homework - submit on

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