IT2101 Computer Architecture

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PREPARING FOR THE BIT
IT2101 Computer Architecture Operating System
caos_at_ict.cmb.ac.lk
Preparing for BIT 26/04/2001
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Major Topics
Review of Basic Principles 07 General System
Architecture 04 Instruction Set Architecture
05 Basic CPU Architecture 04 Memory
Hierarchy I/O Techniques 06 Parallelism
04 Introduction to Operating Systems
04 Processes Process Management 08 Memory
Management 06 File System 06 Unix System
Windows NT Overview 06
Total Lectures 60
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Major Topics

• Review of Basic Principles (7hrs.)
• Radix number systems
• Decimal, Binary, and Hexadecimal number systems
• Binary arithmetic addition, complements, and
  subtraction
• Binary Codes
• BCD code
• ASCII character code
• Boolean algebra and Logic Gates
• Boolean functions
• Logic Gates AND, OR, NOT, NOR, NAND, XOR
• Simplification of Boolean functions(2,3, and 4
  variable Karnaugh maps)

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Review of Basic Principles

• Digital Computer
• A digital system performing computational tasks.
• Represents information using variables that take
  a limited number of discrete values.
• Processes these values internally
• Uses two basic values to represent information

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Radix Number Systems
Each number system has a number of different set
of digits which is called the radix or the base
of the number system.

• Decimal Base 10
• Binary Base 2
• Octal Base 8
• Hexadecimal (Hex) Base 16

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Decimal Number System
Base (Radix) 10 Digits 0, 1, 2, 3, 4, 5, 6, 7,
8, 9 e.g. 747510
The magnitude represented by a digit is decided
by the position of the digit within the number.
For example the digit 7 in the left-most position
of 7475 counts for 7000 and the digit 7 in the
second position from the right counts for 70.
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Binary Number System
Base (Radix) 2 Digits 0, 1 e.g. 11102
The digit 1 in the third position from the right
represents the value 4 and the digit 1 in the
fourth position from the right represents the
value 8.
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Octal Number System
Base (Radix) 8 Digits 0, 1, 2, 3, 4, 5, 6,
7 e.g. 16238
The digit 2 in the second position from the right
represents the value 16 and the digit 1 in the
fourth position from the right represents the
value 512.
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Hexadecimal Number System
Base (Radix) 16 Digits 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, A, B, C, D, E, F e.g. 2F4D 16
The digit F in the third position from the right
represents the value 3840 and the digit D in the
first position from the right represents the
value 1.
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Binary Arithmetic

• Addition
• Complements
• Subtraction

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Binary Addition
0 0 0
0 1 1
1 0 1
1 1 1 0
Carry Bit
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Binary Addition Examples
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Binary Complement (1s Complement) Operation
1 0
0 1
Example 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1
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Twos Complement
The Twos complement of a binary number is
obtained by first complementing the number and
then adding 1 to the result.
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Binary Subtraction
Binary subtraction is implemented by adding the
Twos complement of the number to be subtracted.
Twos complement of 1001
Example 1101 1101 -1001 0111
10100 If there is a carry then it is ignored.
Thus, the answer is 0100.
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Binary Codes
A binary code is a group of n bits that assume up
to 2n distinct combinations of 1s and 0s with
each combination representing one element of the
set that is being coded.

• BCD Binary Coded Decimal
• ASCII American Standard Code for
  Information Interchange

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BCD Binary Coded Decimal
Decimal BCD Number Number 0 0000
1 0001 2 0010 3 0011
4 0100 5 0101 6 0110
7 0111 8 1000 9 1001
When the decimal numbers are represented in BCD,
each decimal digit is represented by the
equivalent BCD code. Example BCD Representation
of Decimal 6349 6 3 4 9 0110
0011 0100 1001
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ASCII
Number ASCII Letter ASCII
0 0110000 1 0110001 2 0110010 3 0110011 4 0110100
5 0110101 6 0110110 7 0110111 8 0111000 9 0111001
A 1000001 B 1000010 C 1000011 D 1000100 E 1000101
F 1000110 G 1000111 H 1001000 I 1001001
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ASCII Continued.
Letter ASCII Letter ASCII
J 1001010 K 1001011 L 1001100 M 1001101 N 1001110
O 1001111 P 1010000 Q 1010001 R 1010010
S 1010011 T 1010100 U 1010101 V 1010110 W 1010111
X 1011000 Y 1011001 Z 1011010
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Logic Gates

• Binary information is represented in digital
  computers by physical quantities called signals.
• Two different electrical voltage levels such as
  3 volts and 0.5 volts may be used to represent
  binary 1 and 0.
• Binary logic deals with binary variables and with
  operations that assume a logical meaning.

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Logic Gates Contd

• A particular logic operation can be described in
  an algebraic or tabular form.
• The manipulation of binary information is done by
  the circuits called logic gates which are blocks
  of hardware that produce signals of binary 1 or 0
  when input logic requirements are satisfied.

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Logic Gates Contd

• Each gate has a distinct graphics symbol and its
  operation can be described by means of an
  algebraic expression or in a form of a table
  called the truth table.
• Each gate has one or more binary inputs and one
  binary output.

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Logic Gates
AND OR NOT (Inverter) NAND (Not AND) NOR
(Not OR) XOR (Exclusive-OR) Exclusive-NOR
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Logic Gates Cont.
AND Logic Gate Truth Table
x A . B
A, B Binary Input Variables x Binary Output
Variable
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Logic Gates Cont.
OR Logic Gate Truth Table
x A B This is read as x equals A or B.
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Logic Gates Cont.
NOT Logic Gate Truth Table
A x 0 1 1 0
x A
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Logic Gates Cont.
NAND Logic Gate Truth Table
x A . B
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Logic Gates Cont.
NOR Logic Gate Truth Table
x A B
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Logic Gates Cont.
XOR Logic Gate Truth Table
A B x 0 0 0 0 1 1 1 0 1 1 1 0
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Logic Gates Cont.
Exclusive-NOR Logic Gate Truth Table
x A B
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Contact

• External Degree Unit (EDU) of the Institute of
  Computer Technology
• No. 221/2A, Dharmapala Mawatha,
• Colombo 7.
• Phone [phone]
• Fax [phone]
• Email bit_at_ict.cmb.ac.lk
• http//www.ict.cmb.ac.lk/bit.htm