C.S. Choy 1

ITM1010 COMPUTER AND COMMUNICATION TECHNOLOGIES

Prof. C.S. Choy, room 412Prof. H.K. Tsang, room 306

Tutors: CY Poon ZJ Zhang CW Lee

SK Cheung

AssignmentsMid-term

Final

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FIRST-HALF TERM SCHEDULE

Week (Monday)8/1 Introduction and Number System15/1 Logic Gates and Boolean Algebra22/1 Chinese New Year29/1 Conference Leave5/2 Digital Design12/2 Sequential Logic Design19/2 Computer Organization

21/3 Mid-term Examination

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RECOMMENDED BOOKS

• Digital Electronics – A Simplified Approach

by R.D. Thompson

Prentice Hall

• The Digital Information Age

by R. Kuc

PWS Publishing

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INFORMATION SYSTEMS

• Process – amplifier, scanner, MP3 player

• Transmit – telephone network

• Store – tape and harddisk

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Why Digital (Binary System)?

• Information IntegrityBetter noise immunity

• Information ManipulationComputer is a binary system and its programmable characteristics offer the greatest flexibility

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SOURCES OF DIGITAL INFORMATION• Analog Signal

• Representation of Number Values

Decimal Binary

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

10 1010

11 1011

12 1100

13 1101

14 1110

15 1111

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BINARY NUMBER SYSTEM

e.g. (1011.11)2=

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BINARY NOTATION

Digit is called BIT.

Possible representations: 1 0

high low

true false

LSB – Least Significant Bit

Bit change with the least effect

HSB – Most Significant Bit

Bit change with the most effect

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BINARY MATHEMATICS

• Addition1101 + 1001 =

1310 + 910 =

• Subtraction– Rules 0 – 0 = 0

1 – 0 = 0

1 – 1 = 0

10 – 1 = 1

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BINARY MATHEMATICS

• Multiplication1101 x 101 =

1310 x 510 =

• Division110111 ÷ 101 =

5510 ÷ 510 =

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SIGNED BINARY NUMBER

Ones (1s) ComplementThe 1s complement of a binary number of a binary number is derived by subtracting each bit in the number to be complemented from 1.

e.g. 1s complement of 1100

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SIGNED BINARY NUMBER

The use of complementary representation allows the subtraction process to be accomplished using addition.

Positive result – high end-round carry

Negative result – low end-round carry

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SIGNED BINARY NUMBERTwos (2s) Complement

The 2s complement of a binary number is the 1s complement plus 1.

Positive result – high carry

Negative result – low carry

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SIGN BITThe use of a single bit, usually the

leftmost bit to indicate the sign of a number. The meaning of the sign bit can be fixed arbitrarily. But normally,

sign bit

0 - positive number 1 - negative number

e.g. -510 = 1101

+510 = 0101

Note: the magnitude of a number is represented by the lower three bits

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SIGN BIT1s Complement 2s Complement

range: -7 – +7 range: -8 – +7

The leftmost bit still indicates sign.

In complement representation, two numbers can be added or subtracted as usual.

e.g. 6 + (-2)

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OVERFLOW CONDITIONSOverflow occurs whenever the sum of two positive numbers yields a negative result or when two negative numbers are summed and the result is positive. Overflow can be detected by the difference in the carry-in and carry-out of the sign bit.

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HEXADECIMAL

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BINARY-CODED DECIMAL BCD

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GRAY CODE

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AMERICAN STANDARD CODE FOR INFORMATION INTERCHANGE, ASCII

The ASCII encodes the letters in the alphabet as well as numbers, it is an alphanumeric code. It is a 7-bit code so allows representation of 128 different characters and commands.

upper-case and lower-case lettersdecimal numberspunctuation marksspecial symbolscommand codes for formatting text

Extended ASCII8-bit code allows for 128 additional graphics

characters.