Computer Architecture and Number Systems

1
Computer Architecture and Number Systems

• Topics
• What is Computer?
• Major Computer Components
• Computer Components Interconnection
• Data Representation
• Bits, Bytes, and Words
• The Decimal Number System
• The Binary Number System
• Converting from Binary to Decimal, Decimal to
  Binary
• The Hexadecimal Number System
• Converting from Hexadecimal to Decimal, Decimal
  to Hexadecimal

2
What is Computer?

• A data processing machine capable of performing
  computations and making logical decisions very
  fast.
• Consists of hardware such as keyboard, screen,
  mouse, disks, memory, CD-ROM, and processing
  units.
• A program (software) is a set of instructions
  written in a computer language that runs on a
  computer.

3
Major Computer Components

• Memory Unit (Main Memory, Secondary Storage Unit)
• Arithmetic and Logic Unit (ALU), Central
  Processing Unit (CPU)
• Input/Output (I/O) Unit

4
Memory Unit

• Memory unit stores information such as computer
  programs, data, or documents.
• Two types of memory devices
• Primary Storage or Main Memory
• Secondary Storage

5
Memory Unit (cont)

• Main memory is fast and expensive .
• Stores frequently accessed information such as
  programs and data during their execution.
• Is volatile storage. That is, if power is lost,
  the information in main memory is lost.
• Secondary storage is slower and cheaper.
• Disks (floppy, hard, removable), Tapes, CDs,
  DVDs.
• Is non-volatile, that is persistent (permanent)
  storage.

6
Memory Unit (cont)

• Main memory consists of a collections of storage
  locations.
• Data are read from or written to memory in cells.
  A cell can be 8 64 bits.
• Address is used to uniquely identify a cell
  location.
• Cells may be grouped into words. E.g., four 8-bit
  cells forms one word.

7
Memory Unit (cont)

• Memory Access Methods
• Sequential access memory
• Read memory address one after another, e.g. tape.
• Random-access memory (RAM)
• Any location can be read by specifying its
  address, e.g. main memory, disks, CDs, DVDs.

8
Input/Output (I/O) Unit

• Input/Output Unit
• Input unit accepts input data and programs from
  an input device.
• Output unit sends the results of processing
  (output) to an output device.
• More generally, these devices are known as
  peripheral devices.
• Input device - keyboard, mouse, scanner
• Output device - monitor, printer
• I/O device - disk drive (floppy, hard,
  removable), CD or DVD drive

9
ALU, CPU

• ALU performs calculations (such as addition,
  subtraction, multiplication, division) and
  logical operations (e.g. comparing two numbers).
• CPU is the brain of the computer.
• Controls operations of other components, memory,
  ALU, I/O.
• Tells input unit when info is ready to be read
  into the memory unit.
• Tells output unit when to send info from the
  memory unit to an output device.

10
Computer Components Interconnection

• CPU and memory are connected by a bus.
• Connecting I/O devices
• I/O devices are slower than CPU/memory.
• Cant connect directly to Bus. Need an I/O
  controller or interface to handle the differences
  in speed between the I/O device and the bus.
• A bus is a group of parallel wires that carry
  control signals and data between CPU and memory.

11
Computer Components Interconnection

• Three types of Bus -
• Data Bus
• Address Bus
• Control Bus
• Data bus consists of many wires. Each wire
  carries 1 bit at a time. The of wires (bits)
  needed size of a word. If the word is 32 bits
  in a computer, then we need 32-bit data bus.

12
Computer Components Interconnection

• Address bus allows access to a particular word in
  a memory. The number of wires log2(total number
  of memory words). If the memory has 2n words,
  address bus needs to carry n bits at a time.
• Control bus carries communication signals between
  CPU and memory. The number of bits used
  log2(total number of control commands).

13
Data Representation

• Data types
• Text
• Number
• Image
• Audio
• Video

14
Bits, Bytes, and Words

• A bit is a single binary digit (a 1 or 0).
• A byte is 8 bits
• A word is 32 bits (that is, 4 bytes)
• Long word 8 bytes 64 bits
• Quad word 16 bytes 128 bits
• Programming languages use these standard number
  of bits when organizing data storage and access.
• What do you call 4 bits? (hint it is a small
  byte)

15
Number Systems

• The data in memory is represented in terms of 1s
  and 0s.
• Therefore, thinking about how information is
  stored in RAM requires knowledge of the binary
  (base 2) number system.
• Lets review the decimal (base 10) number system
  first.

16
The Decimal Number System

• The decimal number system is a positional number
  system.
• Example
• 1 2 6 5 5 X 100 5
• 103 102 101 100 6 X 101 60
• 2 X 102 200
• 1 X 103 1000

17
The Decimal Number System (cont)

• The decimal number system is also known as base
  10. The values of the positions are calculated
  by taking 10 raised to some power.
• Why is the base 10 for decimal numbers?
• Because we use 10 digits, the digits 0 through 9.

18
The Binary Number System

• The binary number system is also known as base 2.
  The values of the positions are calculated by
  taking 2 to some power.
• Why is the base 2 for binary numbers?
• Because we use 2 digits, the digits 0 and 1.

19
The Binary Number System (cont)

• The binary number system is also a positional
  numbering system.
• Instead of using ten digits, 0 - 9, the binary
  system uses only two digits, 0 and 1.
• Example of a binary number and the values of the
  positions
• 1 0 0 1 1 0 1
• 26 25 24 23 22 21
  20

20
Converting from Binary to Decimal

• 1 0 0 1 0 0 1 1 X 20 1
• 26 25 24 23 22 21 20 0 X 21 0
• 0 X 22 0
• 20 1 24 16 1 X 23 8
• 21 2 25 32 0 X 24 0
• 22 4 26 64 0 X 25 0
• 23 8 1 X 26 64 7310

21
Converting from Binary to Decimal (cont)

• Practice conversions
• Binary Decimal
• 101
• 1101
• 101101

22
Converting From Decimal to Binary (cont)

• Perform successive divisions by 2, placing the
  remainder (0 or 1) in each of the positions from
  right to left.
• Continue until the quotient is zero.
• Example 4410
• 44 / 2 22 rem 0
• 22 / 2 11 rem 0
• 11 / 2 5 rem 1
• 5 / 2 2 rem 1
• 2 / 2 1 rem 0
• 1 / 2 0 rem 1
• Done answer 1 0 1 1 0 0 2
  

23
Converting From Decimal to Binary (cont)

• Practice conversions
• Decimal Binary
• 59
• 82
• 175

24
Working with Large Numbers

• 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 ?
• Humans dont work well with binary numbers there
  are too many digits to deal with.
• Memory addresses and other data can be quite
  large. Therefore, we sometimes use the
  hexadecimal number system.

25
The Hexadecimal Number System

• The hexadecimal (hex) number system is also known
  as base 16. The values of the positions are
  calculated by taking 16 to some power.
• Why is the base 16 for hexadecimal numbers ?
• Because we use 16 symbols, the digits 0 and 1 and
  the letters A through F.

26
The Hexadecimal Number System (cont)

• Example of a hexadecimal number and the values of
  the positions
• 3 C 8 B 0 5 1
• 166 165 164 163 162 161 160

27
The Hexadecimal Number System (cont)

• Binary Decimal Hexadecimal Binary
  Decimal Hexadecimal
• 0 0 0
  1010 10 A
• 1 1 1
  1011 11 B
• 10 2 2
  1100 12 C
• 11 3 3
  1101 13 D
• 100 4 4
  1110 14 E
• 101 5 5
  1111 15 F
• 110 6 6
• 111 7 7
• 1000 8 8
• 1001 9 9

28
Converting From Hexadecimal to Decimal

• Example Convert 1A5F16 to decimal.
• 1 A 5 F
• 163 162 161 160
• 4096 256 16 1
• Recall A16 1010 and F16 1510.
• 1 x 4096 A x 256 5 x 16 F x 1
• 1 x 4096 10 x 256 5 x 16 15 x 1
• 4096 2560 80 15
• 675110

29
Converting From Decimal to Hexadeciaml

• Perform successive divisions by 16, placing the
  remainder (0-9, A-F) in each of the positions
  from right to left.
• Continue until the quotient is zero.
• Example Convert 14310 to hex.
• 143 / 16 8 rem 1510 F16
• 8 / 16 0 rem 8
• Done answer 8F16
• To Check 8 x 16 15 128 15 14310

30
Example of Equivalent Numbers

• Binary 1 0 1 0 0 0 0 1 0 1 0 0 1 1 12
• Decimal 2064710
• Hexadecimal 50A716
• Notice that the number of digits needed is
  smaller as the base increases.

31
Next Class

• Operating System and Using Linux.
• Homework 1 due beginning of class on September 9.