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How Computers Represent Data

- Computers work with binary numbers, which include only 0s and 1s.
- smallest piece of data a computer can work with is known as a bit.
- A bit is either “on” or “off,” a 0 or a 1.
byte : Eight bits , signify a single unit of storage.
data transfer rate : bits per second, such as gigabits per second (Gbps).
measurement of data : bytes, such as gigabytes (GB).
hexadecimal (hex) numbers: the numbers 0 through 9, followed by letters A through F.

why does the computers convert binary numbers into hexadecimal (hex) numbers?
Because even small numbers require many digits when converted to binary

Floating-point notation

Has no fixed Enables a computer

number of digits to work speedily Requires special
before or after a with very large or processing circuitry
decimal point small numbers

Characters (letters, numbers, and symbols) are converted into numbers the computer
understands , Character code performs this conversion.

American Standard Extended Binary Coded

Code for Information Decimal Interchange Unicode
Interchange (ASCII ) Code (EBCDIC)

Three main types of character coding are

Convert decimal into binary :

Start by making a chart. List the powers of two in a "base 2 table" from right to left. Start at
20, evaluating it as "1". Increment the exponent by one for each power. Make the list up
until you've reached a number very near the decimal system number you're starting with.
Example : convert the decimal number 16 to binary.

power of 2: 23 22 21 20
- 8 4 2 1
binary 1 1 1 0
number:

1610 = 11102
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Convert binary into decimal :

the decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
decimal = d0×20 + d1×21 + d2×22 + ...
Example
Find the decimal value of 1110012:

binary
1 1 1 0 0 1
number:
power of
25 24 23 22 21 20
2:

1110012 = 1x25+1x24+1x23+0x22+0x21+1x20 = 5710

Convert decimal into hexadecimal :
Divide the number by 16.
Example
Convert 756210 to hex:

Division Quotient Remainder Remainder * Remainder

by 16 (integer) (decimal) 16 (hex)
7562/16 472 0.625 10 A
472/16 29 0.5 8 8
29/16 1 0.8125 13 D
1/16 0 0.0625 1 3

Convert hexadecimal into decimal :

A regular decimal number is the sum of the digits multiplied with power of 10.
137 in base 10 is equal to each digit multiplied with its corresponding power of 10:
13710 = 1×102+3×101+7×100 = 100+30+7
Hex numbers are read the same way, but each digit counts power of 16 instead of power
of 10.
For hex number with n digits:
Dn-1 ... d3 d2 d1 d0
Multiply each digit of the hex number with its corresponding power of 16 and sum:
decimal = dn-1×16n-1 + ... + d3×163 + d2×162 + d1×161+d0×160

Example
E7A9 in base 16 is equal to each digit multiplied with its corresponding 16n:

Hex number E 7 a 9
‫رقمه‬ 14 7 10 9
163 162 161 160
E7A916 = 14×163 + 7×162 + 10×161 + 9×160 = 57344+1792+160+9 = 59305 10

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convert binary to hex , or hex to binary:

binary hex
0000 0
0001 1
0010 2 Convert every 4 binary digits (start from
0011 3 bit 0) to 1 hex digit, with this table:
0100 4
Example
0101 5
Convert binary 11011002 to hex:
0110 6
Convert every 4 binary bits (from
0111 7 bit0) to hex digit:
1000 8 11011002 = 110 1100
1001 9 = 0110 1100 = 6 C = 6C16
1010 A
1011 B Example 2
1100 C Convert hex 5B16 to binary:
1101 D 5B16 = 5 B = 101 1011 = 10110112
1110 E
1111 F

Introducing the System Unit

system unit : the case that contains the major hardware components of a computer.
- It come in different styles and have varying footprints
Footprints : the amount of space that the unit uses.
- Some units have embedded biometric authentication devices.
- System units vary in their form factor, which specifies how the internal components
are located within the system unit.

Mother Power Cooling Internal Drive

CPU Expansion
board Supply fan speaker bays
slots

System unit main components

What’s on the Motherboard?
Motherboard : the printed circuit board that contains the electrical circuitry for the
computer.

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integrated circuits : The majority of parts found on the motherboard

An integrated circuit (or chip) includes millions of transistors and carries electrical current.
A transistor : a switch that is able to control the electrical signal flow to the circuit.

central processing unit (CPU).

central processing unit (CPU) : The integrated circuit chip that processes electronic
signals , its known as a microprocessor or processor or Core.
Instruction : the specific number Each operation performed by the CPU
instruction set : the list of CPU instructions for the operations that it performs.

machine
cycle or
processing
cycle The two main
parts of the
CPU are the
control unit and
the arithmetic
logic unit.
control
unit

• control unit retrieves instructions from memory and interprets and performs those
instructions.
• The control unit manages the machine cycle or processing cycle, the four-part
process performed by the CPU.
The control unit manages four operations

Decode Store
•Retrieves •Performs the
•Determines what • Stores the results
program the program is requested action to an internal
instructions telling the register
computer to do

Fetch Execute
arithmetic logic unit (ALU) : performs arithmetic and logical operations.
- Arithmetic operations involve adding, subtracting, multiplying, and dividing.
- Logical operations involve comparisons between two or more data items.

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- Registers store data when it must be temporarily stored in the CPU.

Factors that affect the performance of a CPU include:
• The number of existing transistors
• Data bus width and word size
• Clock speed
• Operations per microprocessor cycle
• Use of parallel processing
• Type of chip
data bus : group of parallel wires that connect the CPU’s internal components.
Data bus width is measured in bits.
word size : The maximum number of bits the CPU can process at once
Word size determines which operating systems and software a CPU can run.

system clock
- system clock : an electronic circuit that produces rapid pulses and coordinates the
computer’s internal activities.
- Clock speed : the measurement of the electrical pulses generated by the system
- Clock speed measured in gigahertz (GHz).
- the higher the clock speed, the faster the computer.
- The number of operations per tick of the system clock affects microprocessor
performance.
- Superscalar architecture enables the CPU to perform more than one instruction for
each clock cycle.
- Pipelining enables the CPU to process more than one instruction at a time, which
improves CPU performance
Parallel processing : a method in which more than one processor performs at the same
time, resulting in faster processing.
chipset : set of chips that collectively supply the switching circuitry the CPU requires to
move data throughout the computer

Random access memory (RAM)

Temporarily stores data and instructions; to be used by the central processing unit .
Why the RAM considered as a volatile ?
because its contents are erased when the computer is shut off .
What allows Permits the CPU to access or store data and instructions quickly through RAM ?
RAM’s memory address feature, which is a way to identify and locate stored data .
read-only memory (ROM)
ROM : Contains prerecorded instructions used to start the computer
- Is considered nonvolatile because its contents are stored when CPU power is turned
off

Cache memory

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Cache memory : a small unit of fast memory built into the processor to improve
performance
Rom Is more expensive than RAM m and it Comes in two types:

Secondary cache,
Primary cache, found in
located on the circuit
the microprocessor chip
board

What’s on the Outside of the Box?

The front panel includes:

drive activity light,

power switch, which is power-on light, which
which advises the user
used to turn the shows whether or not
that the hard drive is
computer on the power is on
retrieving data

Other features on the outside of a system unit:

port : an interface used to send data into and retrieve data from the computer. An example
is a USB port.
connector : a physical receptacle where the user can plug a peripheral device into the
computer. An example is a telephone jack.
Legacy technology is older technology that is being phased out. Examples are:

SCSI (small
Parallel computer
Serial ports ports PS/2 ports
ports system
interface)

Mariam’s notes for chapter 2 3 ‫قل تكفى وبعطيك نوتز شابتر‬