Leeds College of Technology
National Diploma for IT Practitioners (Networking Level 3)
Unit 9 – Computer Architecture
Unit Tutor: [OMITTED]
Name: Tat Ho
Tat Ho
Computer Architecture
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10 March 2009
Tat Ho
Computer Architecture
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Contents:
1.1 Number Systems................................................................... 3
- Notation........................................................................................ 3
- The Base Number........................................................................
4
- How number systems are stored in memory................................ 4
- Binary Coded Decimal (BCD) ....................... .............................. 4
1.2 Analogue to Digital Conversion.......................................... 5
- Method of Conversion………………………………………...........
5
1.3 Decimal and Hexadecimal Conversion............................... 6
1.4 Arithmetic Hexadecimal operations.................................... 7
2.1 Logic Gates........................................................................... 9
2.2 A-Stable and Bi-Stable Flip Flops....................................... 13
2.3 Prototype for a Process Control System........................... 15
- Truth Table.................................................................................
15
- Output........................................................................................
15
- Boolean Terms and Expressions...............................................
15
- Logic Circuit (Unsimplified).........................................................
16
- Karnaugh Map............................................................................
17
- Simplified Expression.................................................................
17
- Logical Circuit (Simplified)..........................................................
17
- Evaluation...................................................................................
17
2.4 Features of a Processor.......................................................... 19
- Key Components of Computer Architecture...............................
19
- Fetch Execute Cycle...................................................................
20
- Comparing and Contrasting Two Processors..............................
24
3.1 SMS Program Simulator.............................................................. 25
3.2 SMS Traffic Light Simulator....................................................... 29
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Computer Architecture
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Computer Architecture
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Subtask 1.1 (P1)
Describe using examples how numeric and alphanumeric data can be coded
within a computer system.
Numeric and alphanumeric data within a computer system can be coded in
several ways. One method in which, uses what we call number systems in
order to represent values.
Number Systems Part I:
A number system is a defined system in which we use to represent numerical
values. Values in number systems can be converted from one to another and
vice versa. For example the most common number system of today is the
decimal number system. You can convert a decimal value into a hexadecimal
value.
Other forms of number systems that are used in computing are Hexadecimal,
Octal and Binary. The following table will show how a decimal number system
relates in respect to the other number systems.
Notation:
You will notice that to avoid confusion, the number notation is xy (x to the base
y), with the base number always written as a subscript.
Binary (Base 2)
Octal (Base 8)
Decimal (Base
10)
Hexadecimal
(Base 16)
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
00 (000)
01 (001)
02 (010)
03 (011)
04 (100)
05 (101)
06 (110)
07 (111)
10 (001) (000)
11 (001) (001)
12 (001) (010)
13 (001) (011)
14 (001) (100)
15 (001) (101)
16 (001) (110)
17 (001) (111)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
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Computer Architecture
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The Base Number:
Each number system will have a base number. The following table will show
you the relationships between the base number and the range of values that
specific number system can take.
Number
System
Range of
Values
Number of
Digits
Base
Number
Binary
Octal
Decimal
Hexadecimal
0–1
0–7
0–9
0–F
2
8
10
16
2
8
10
16
Number Systems Part II:
Binary: Has two digits consisting of values ranging from 0-1, and has 2
different unique characters. The binary place values can be represented in the
following table:
28
27
26
25
24
23
22
21
128
64
32
16
8
4
2
1
Octal: Has eight digits consisting of values ranging from 0-7, and has 8
different unique characters. The way an octal value is written is in a series of
three binary digits. Notice that the values of 8 and 9 are not recognised as
only the numbers 0-7 are used.
Decimal: Has ten digits consisting of values ranging from 0-9, and has 10
different unique characters.
Hexadecimal: Has sixteen digits consisting of values ranging from 0-9,
followed by
A-F and has 16 different unique characters.
How Number Systems are Stored in Memory:
When you wish to store data in memory, there are a few things you have to
consider which are the entities address and the data location.
The way information is stored is dependant on the width of the bus. For
example a 16bit data on a 4bit bus will require it to be sent in parts of 4.
Binary Coded Decimal
This is a 4 bit representation of numerical values as shown in the table below:
Decimal 0
1
2
3
4
5
6
7
8
9
Digit
BCD
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001
Code
For example to represent 55 in BCD this will be: 0101 0101.
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Computer Architecture
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Data Storage in a Computer:
Location
Contents 1
0
0
0
204
0
0
1
0
0
1
0
0
205
1
0
0
1
This is how data is stored in RAM. The location 204 and 205 are each
segment of a set space in RAM. The contents can hold up to 8 bits of
information. As you can see above, 4 BCD’s can be stored in the two
locations.
Characters in ASCII:
In order to represent characters in binary, you would have to convert the
binary value into a decimal value. You will then use each of the characters to
represent a BCD code for each. If I were to represent the word ‘binary’, this
would be;
ASCII Character
b
i
n
a
r
y
Tat Ho
Binary
01100010
01101001
01101110
01100001
01110010
01111001
Decimal
98
105
110
97
114
121
Computer Architecture
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BCD Code
1001 1000
0001 0000 0101
0001 0001 0000
1001 0111
0001 0001 0100
0001 0010 0001
10 March 2009
Subtask 1.2 (P2)
Describe how analogue data can be converted and stored in computer
systems.
[OMITTED]
Tat Ho
Computer Architecture
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Subtask 1.3 (P3)
The following data is stored in memory locations in an 8-bit memory store.
Convert each binary number into decimal and hexadecimal.
[OMITTED]
Tat Ho
Computer Architecture
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Subtask 1.4 (P4)
Convert the following hexadecimal into binary and perform the operations
shown using 2’s complement arithmetic where appropriate.
Reconvert the results to hexadecimal.
[OMITTED]
Tat Ho
Computer Architecture
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Task 2
Subtask 2.1 (P7)
Describe with the aid of truth tables, the operation of six basic logic gates. For
each gate include the logic symbol and logic expression.
A logic gate is one in which performs a logical operation. In the following I will
go through the six main ones that are used universally.
Gate
Truth Table
NOT
INPUT OUTPUT
A
NOT A
0
1
1
0
Symbol
Description
Gate
Truth Table
This gate inverts the output of the
gate. It is most commonly known as
an inverter. Therefore a 1 input
results in a 0 output, conversely a 0
input results in a 1 output.
AND
INPUT OUTPUT
A B A AND B
0 0
0
0 1
0
1 0
0
1 1
1
Symbol
Description
Tat Ho
This gate only produces an output
when all the inputs are 1.
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Gate
Truth Table
OR
INPUT OUTPUT
A B
A+B
0 0
0
0 1
1
1 0
1
1 1
1
Symbol
Description
Gate
Truth Table
This gate produces a 1 output when
the conditions of having a 1 in the
input are met.
NAND
INPUT OUTPUT
A B A NAND B
0 0
1
0 1
1
1 0
1
1 1
0
Symbol
Description
Tat Ho
Opposite of AND with inverter at the
end. This can be considered as a
combination of the AND and NOT
gate. This gate produces a 1 output in
any combination except from 1 and 1.
Computer Architecture
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Gate
Truth Table
NOR
INPUT OUTPUT
A B A NOR B
0 0
1
0 1
0
1 0
0
1 1
0
Symbol
Description
Gate
Truth Table
Opposite of OR with inverter at the
end. This can be considered as a
combination of the OR and NOT gate.
This gate produces an output when
there is no input to this gate (i.e. both
are 0).
XOR
INPUT OUTPUT
A B A XOR B
0 0
0
0 1
1
1 0
1
1 1
0
Symbol
Description
Tat Ho
This gate produces a 1 output when
the inputs are not identical. i.e. both
are 0 or 1.
Computer Architecture
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Gate
Truth Table
XNOR
INPUT OUTPUT
A B A XNOR B
0 0
1
0 1
0
1 0
0
1 1
1
Symbol
Description
Tat Ho
This gate produces a 1 output when
both the inputs are the same.
Computer Architecture
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Subtask 2.2 (M4)
Describe the difference between an a-stable and a bi-stable flip-flop. Explain
how these devices are used as memory elements and a computer clock
source.
A-stable:
This circuit is a free running oscillator. It oscillates between two states at a
certain frequency defined by the clock cycle intervals in the circuit itself. This
then generates a wave output that can be described as a ‘square wave’.
Another example of an a-stable circuit is the 555 integrated circuit. The IC can
produce very accurate oscillations used in popular applications.
The diagram below shows the configuration of an a-stable flip flop consisting
of an oscillator, a switch and an ‘AND’ gate. There is a buzzer to indicate that
the circuit is functioning.
This is a universal 555 timer
which is implemented in many
circuit boards.
Bi-stable:
This circuit is defined by having a state that is either on or off. It remains in
this state until one of the switches is activated.
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Computer Architecture
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It is also called a ‘flip-flop’. The bi-stable circuit provides uses in several
applications such as frequency dividers, counters, or a storage device in
computer memory.
In order to store data in a memory location, you would implement the use of a
bi-stable circuit. For example the data below will be stored unless the ‘reset’
switch is activated.
0
Tat Ho
1
0
1
1
0
1
0
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Subtask 2.3 (M2, D1)
Design a prototype for a process control system with the aid of the following:
- Truth Table
- Output
- Boolean Terms and Expressions
- Logic Circuit (Unsimplified)
- Karnaugh Map
- Simplified Expression
- Logical Circuit (Simplified)
- Evaluation
The specification states that the system has four inputs (A, B, C, D) with a
single output (X). The system will be used to check a four-bit binary (word)
number within the HEX range 0 to F. A being the most significant and D the
least significant bit.
The output will produce a logic ‘1’ at the output (X) whenever an odd number
is detected. NOTE: HEX Value F ignored.
Truth Table:
Variable A
B
C
D
0
1
2
3
4
5
6
7
8
9
10 (A)
11 (B)
12 (C)
13 (D)
14 (E)
15 (F)
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
O/P
Terms
1
A∙B∙C∙D
1
A∙B∙C∙D
1
A∙B∙C∙D
1
A∙B∙C∙D
1
A∙B∙C∙D
1
A∙B∙C∙D
1
A∙B∙C∙D
EXP = A∙B∙C∙D + A∙B∙C∙D + A∙B∙C∙D + A∙B∙C∙D + A∙B∙C∙D + A∙B∙C∙D +
A∙B∙C∙D
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Computer Architecture
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Logical Circuit (Unsimplified):
The above shows an unsimplified version of the logical circuit.
- The switches are all switched on.
- The output can be seen from the 7 segment LED.
- The LED indicator shows that there is no output value.
- The oscillator makes the LED appear to be flashing.
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Computer Architecture
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Karnaugh Map:
a = C∙D
b = A.D
c = A.B.D
EXP = C∙D + A.D + A.B.D
Simplified Expression: D(A + AB + C)
Logical Circuit:
Evaluation:
Using the Karnaugh Map process is to create a more simplified circuit. This is
highly beneficial due to the significantly fewer gates used in the processed
circuit for example in the above circuits, the original gates used were 23,
whereas using the Karnaugh Map, we reduced to to 8. It can reduce costs to
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Computer Architecture
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manufacturers if there is a complex circuit involving several hundred logical
gates. Another advantage of having reduced number of gates is that it is
easier to service and allows more space for more functionality. Fault finding
would be far more easier compared to the more complex un-simplified version
of the circuit.
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Computer Architecture
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Subtask 2.4 (P5, P6, M1, D2)
Describe the key components of computer architecture and how they interact.
(P5)
Produce a section in your report which describes, with the aid of diagrams,
(including logic gates, registers, buses, PC, Control unit, ALU and Memory)
the features of a processor and how data travels around the processor. (P6,
M1)
Compare and contrast two different processors. (D2).
Key Components of Computer Architecture:
[OMITTED]
The control unit controls the flow of data going though the processor. The
Arithmetic Logic Unit performs mathematical operations.
Fetch Execute Cycle Part I:
Logic gates are a set of
predefined gates that
produce a series of
operations.
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Computer Architecture
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Fetch Execute Cycle II:
Control
Bus
Data
Bus
Address
Bus
This represents the
allocation slots in
RAM (memory)
[OMITTED]
[OMITTED]
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[OMITTED]
[OMITTED]
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[OMITTED]
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Comparing and Contrasting Two Processors:
[OMITTED]
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Task 3
Subtask 3.1
Simple Addition
[OMITTED]
Registered the value of AL.
Registered the value of BL.
Result is shown in register AL.
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Computer Architecture
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Simple Subtraction
[OMITTED]
Registered the value of AL.
Registered the value of BL.
Result is shown in register AL.
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Computer Architecture
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Simple Multiplication
[OMITTED]
Registered the value of AL.
Registered the value of BL.
Result is shown in register AL.
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Computer Architecture
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Simple Division
[OMITTED]
Registered the value of AL.
Registered the value of BL.
Result is shown in register AL.
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Computer Architecture
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Subtask 3.2
Traffic Light Sequence Control Truth Table
Seq Lights
EW
1
R
2
RA
3
G
4
A
5
R
6
R
7
R
8
R
9
R
On
NS
R
R
R
R
R
RA
G
A
R
Hex
90
D0
30
50
90
98
84
88
90
EW (East West )
R
A
G
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
NS (North South)
R
A
G
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
Spare
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Source code for traffic light system:
[OMITTED]
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Computer Architecture
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- Registers:
These can be considered as data stores that stores data from the code
a user defines – and is then executed. Currently you can see the AL
register with the value of 10010000 (90) and the BL register with the
value 00010101 (15).
- Traffic Light Simulation:
This is a real-time simulation that shows you visually what commands
are being executed in order to produce specific lights to be turned on.
Currently both red lights are turned on.
- RAM Hexadecimal View:
This shows you the current entries stored in RAM. There are three
views, namely; X Hexadecimal, Y ASCII, Z Source.
c
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Currently you can see the AL register with the value of 11010000 (D0) and the
BL register with the value 00010101 (15). This represents RED + AMBER,
and RED. Notice that in the RAM hexadecimal view the pointer has moved to
the next set of instructions.
[OMITTED]
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