1. Computer Organization
Introduction- Digital Systems and Binary Systems
week1

2. Agenda Course books Course outline Digital Systems :
Definition, features
Examples
MAIN USE OF DIGITAL SYSTEMS
Digital via Analog
DIGITAL SYSTEMS - TWO CLASSES
Number Systems:
Decimal weight
Binary representation
Conversion binary to decimal and decimal to binary
Binary to hexadecimal conversion
Decimal conversion to Hexadecimal
Octal conversion to other systems

3. Course books: Digital Design, M. Morris Mano, Prentice-Hall.
Computer Organization and Architecture, 7th Edition, William Stalling, Prentice-Hall.

4. Course contents:
Number system:(Different number systems, conversion and arithmetic operations)
Logic gates, Boolean algebra and arithmetic logic circuits:(basic logic gates, laws of Boolean algebra, deriving logical expression, simplifying logic expressions, half and Full adders, binary coded decimal adder, subtractor)
Logic devices:(Comparator, Decoder, Encoder, multiplexer)
Flip Flops and Counter:(S-R, J-K and D F/F’s in addition to counter design)

5. chapter 3: Buses and Computer Architecture (Processor prototype design, program simulation, computer component interconnection and interrupt)
Chapter 4 : Cache memory (Introduction, mapping and cache design and managements)
chapter 9: Computer Arithmetic
Chapter 10: Instruction Sets: Characteristics and Functions
Chapter 11: Instruction Sets: Addressing Modes and Format
Chapter 7: Input/Output

6. Digital Systems Computers work with just 1s and 0s.
Groups of bits can be made to represent discrete symbols which are then used to develop digital system using different techniques.
Digital system is a system that manipulates discrete elements of information represented internally in binary form/code(1s and 0s).
Digital computers are powerful (why?) it can perform not only arithmetic computations but also logical operations and it can be programmed to make decisions based on internal and external conditions.

7. Digital Systems Reliability: error-correcting codes
Cost decrease: Same hardware can be re- programmed to be used in another application. Number of transistors that can be put on a piece of silicon increases to produce complex functions, the cost per unit decreases and the speed is extremely high
Example: DVD where audio, video and other data can be recorded without any loss of data.

8. MAIN USE OF DIGITAL SYSTEMS:
INFORMATION PROCESSING (text, audio, visual, video)
TRANSMISSION (communication)
STORAGE

9. Digital via Analog Digital Analog Inputs and outputs
finite number of discrete values
from a continuous
(infinite) set
Example
Digital vs. analog scale for measuring weights

10. DIGITAL SYSTEMS - TWO CLASSES:
COMBINATIONAL
SYSTEMS
z(t) = F(x(t))
SEQUENTIAL
z(t) = F(x(0;t))
Memory
No memory
Has memory
Output
Does not depend on previous inputs
x(0;t): input sequence from time 0 to time t
z(t) depends also on previous inputs(memory)
Example from real life
A system with three inputs, A, B, and C, and one output Z, such that Z = 1 if and only if two of the inputs are 1
A traffic controller on two streets: the light is green on each street for a fixed period of time, then goes to yellow for another fixed period and finally to red. The only input to this system is the clock and there are six outputs, one for each color

11. Number system: 1. Decimal
Numbers consist of a bunch of digits, each with a weight
These weights are all powers of the base, which is We can rewrite this:
To find the decimal value of a number, multiply each digit by its weight and sum the products. 1 6 2 . 3 7 5
Digits
100 10
1/10
1/100
1/1000
weight 1 6 2 . 3 7 5
Digits
102
101
100
10-1
10-2
10-3
weight
(1 x 102) + (6 x 101) + (2 x 100) + (3 x 10-1) + (7 x 10-2) + (5 x 10-3) =

12. 2. Binary:
Binary representation:

13. 2.1 Convert from binary to decimal:
Example 1: to decimal ?
multiply each digit by its weight and sum the products.
Digital design book page 21
1* * * * *23 + 1*22 + 0*21 + 1*20
1* * *32 + 1*16 + 1*8 + 1* * 2 + 1* 1
157

14. Binary : Example 2 :Convert the binary 1101.01 to decimal.
Binary digits, or bits
Weights (in base 2)
The decimal value is:
(1 x 23) + (1 x 22) + (0 x 21) + (1 x 20) + (0 x 2-1) + (1 x 2-2) =
= 13.25

15. 2.2 Convert from decimal to binary:
To convert a decimal integer into binary, keep dividing by 2 until the quotient is 0. Collect the remainders in reverse order.
To convert a fraction, keep multiplying the fractional part by 2 until it becomes 0. Collect the integer parts in forward order.
Example 1: :
So, =
162 / 2 = 81 rem 0
81 / 2 = 40 rem 1
40 / 2 = 20 rem 0
20 / 2 = 10 rem 0
10 / 2 = 5 rem 0
5 / 2 = 2 rem 1
2 / 2 = 1 rem 0
1 / 2 = 0 rem 1
0.375 x 2 = 0.750
0.750 x 2 = 1.500
0.500 x 2 = 1.000

16. Example 2:

17. 3. Hexadecimal(base 16): Numbers in hexadecimal system :
A B C D E F
Is frequently used to specify
things like 32-bit IP addresses
and 24-bit colors.

18. 3.1 convert hexadecimal to binary:
Replace each hex digit with its equivalent 4-bit binary sequence.
3.2 convert binary to hexadecimal:
To convert from binary to hex, make groups of 4 bits, starting from the binary point. Add 0s to the ends of the number if needed. Then, just convert each bit group to its corresponding hex digit. = = =
= B C16
1111 F
1011 B
0111 7
0011 3
1110 E
1010 A
0110 6
0010 2
1101 D
1001 9
0101 5
0001 1
1100 C
1000 8
0100 4
0000
Binary
Hex

19. 3.3 convert from hexadecimal to decimal:
Example 3:
Convert from decimal to hex
764= ?