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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

3.4 Addition and subtraction of different number representations

Class work:

2's complement

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