Introduction to Computer
1
Science
With Examples in Visual Basic, C,
C++, and Java
1Mata-Toledo,
Ramon A. & Cushman, Pauline K.
McGraw-Hill, Copyright@2000
Computers
• Computer: a device which, under the direction of
a program, can process data, alter its own program
instructions, and perform computations and logical
operations without human intervention
– Two different levels: architecture and its
implementation
• Architecture: user-visible interface as seen by the programmer
• Implementation: Construction of that interface using specific
hardware and software components
Program
• Refers to a specific set of instructions give
to the computer to accomplish a specific
task
Computer Structures
1. High-speed memory unit
2. Central Processing Unit (CPU)
3. Peripheral (I/O Subsystem)
Basic Computer Structure
Keyboard
Input & Output bus
Control
Unit
Arithmetic
Logic Unit
General
Registers
Program
Counter
R0
R1
Status
Register
Primary
Memory
I/O Bus
Memory Unit
• Main or physical memory – where all the
instructions and data that the CPU can directly
access and execute
– Known as RAM (Random Access Memory)
• Divided into logical units of the same size
– Called a byte; 8 consecutive bits or binary digits
• Can be magnetized to one of two states (on or off) 1or 0
• Each byte is associated with a unique address
– Which can increase right to left or left to right
Address Space
• Set of all unique addresses that a program can
reference
– The address of a byte is fixed whereas its content will
vary
– Number of bits used to represent the address determines
the size of the address space
• Calculated as 2N where N is the number of bits used to
represent the address
– The size of the memory of a computer is measured in
bytes
Memory Units
•
•
•
•
•
•
1 nibble
1 byte
1 word
1 long word
1 quad word
1 octa-word
•
•
•
•
•
•
8 consecutive bits
4 consecutive bits
2 consecutive bytes
4 consecutive bytes
8 consecutive bytes
16 consecutive bytes
Larger Units of Memory
•
•
•
•
•
•
1 Kilobyte
1 Megabyte
1 Gigabyte
1 Terabyte
1 Petabyte
1 Exabyte
•
•
•
•
•
•
1024 bytes
~106 bytes
~109 bytes
~1012 bytes
~1015 bytes
~1018 bytes
32 Mb = 32*103 Kb = 32 * 103 *1024 bytes = 32,768,000 bytes
Central Processing Unit
• Brain of the computer
– Fetching instructions from memory and executing them
• Divided into
– Arithmetic Logic Unit (ALU)
• Additions, subtractions, comparisons
– Control Unit (CU)
• Manages movement of data within the processor
• Contains general registers that provide local highspeed storage for the processor
• Contains status registers that provide information
about the state of the processor, the instruction
being processed and any special circumstances
Sample Processing Sequence
•
Two numbers in main memory are added
1.
2.
3.
4.
Instruction is transferred from memory into the CPU
Location of the instruction being processed is updated in the
instruction counter (IC) or program counter (PC)
The instruction just fetched is stored in the instruction
register (IR)
CU decodes the instruction to add two numbers
•
•
5.
6.
7.
8.
9.
operator [operand1], [operand2], [operand3]
ADDW3 first_no, second_no, answer
• W = words, 3 = no of operands in the instruction
Numbers are located in main memory
Fetched into internal registers of the ALU by the CU
Addition is carried out by ALU
Sum stored in new memory location by CU
The IC is updated to point to the next instruction
Communication
• During the process of described, two additional
registers facilitate the communication between the
CPU and main memory
– Memory address register (MAR)
• Holds the address to or from which the data is being
transferred
– Memory data register (MDR)
• Contains the data to be written into or read out of the address
location
I/O
• Most common input devices
– Keyboard
– Mouse
• Most common output devices
– Monitor
– Printer
• Dual purpose
–
–
–
–
Hard drives
Tapes
Jazz or Zip Drives
Floppies
Bus Structure
•
BUS: A collection of wires to transfer data
within different components of a computer
–
Generally 3 such busses
1. Address bus
2. Data Bus
•
Must have as many wires as ther are bits of data in the
memory unit of the computer
3. Control bus
Destructive Operations
• If a location isn’t specified for a result, it is
often stored in the second operand
– A destructive operation
• If a location is specified for a result, it is
used
– A non-destructive operation
Representing Data
• The computer knows the type of data stored
in a particular location from the context in
which the data are being used; i.e.
individual bytes, a word, a longword, etc
– 01100011 01100101 01000100 01000000
• Bytes: 64(10, 68 (10, 101 (10, 99(10
• Two byte words: 17,472 (10 and 24,445 (10
• Longword: 1,667,580,992 (10
Number Systems and Codes
• We use the DECIMAL (10 system
• Computes use BINARY (2 or some shorthand for it
like OCTAL (8 or HEXADECIMAL (16
• Given any positive integer basis or (RADIX) N,
there are N different individual symbols that can be
used to write numbers in the system. The value of
these symbols range from 0 to N-1
• All systems we use in computing are positional
systems
– 495 = 400 + 90 +5
Conversions
Decimal
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Binary
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Octal
1
2
3
4
5
6
7
10
11
12
13
14
15
16
17
Hex
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
Decimal Equivalents
•
Assuming the bits are unsigned, the decimal
value represented by the bits of a byte can be
calculated as follows:
1. Number the bits beginning on the right using
superscripts beginning with 0 and increasing as you
move left. Remember, 20, by definition is 1
2. Use each superscript as an exponent of a power of 2
3. Multiply the value of each bit by its corresponding
power of 2
4. Add the products obtained
Horner’s Method
• Another procedure to calculate the decimal
equivalent of a binary number
– This method works with any base
• Horner’s Method:
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–
–
–
–
Step 1: Start with the first digit on the left
Step 2: Multiply it by the base
Step 3: Add the next digit
Step 4: Multiply the sum by the base
Step 5: Continue the process until you add the last digit
Hex to Binary
• Step 1: Form four-bit groups beginning from the
rightmost bit of the binary number
– If the last group (at the leftmost position) has less than
four bits, add extra zeros to the left of the group to
make it a four-bit group
• 0110011110101010100111 becomes
• 0001 1001 1110 1010 1010 0111
• Step 2: Replace each four-bit group by its
hexadecimal equivalent
– 19EAA7(16
Converting Decimal to Other Bases
• Step 1: Divide the number by the base you are
converting to (r)
• Step 2: Successively divide the quotients by (r)
until a zero quotient is obtained
• Step 3: The decimal equivalent is obtained by
writing the remainders of the successive division
in the opposite order in which they were obtained
– Know as modulus arithmetic
• Step 4: Verify the result by multiplying it out
Addition & Subtraction Terms
• A+B
– A is the augend
– B is the addend
• C–D
– C is the minuend
– D is the subtrahend
Addition Rules
Addition
• Step 1: Add a column of numbers
• Step 2: Determine if there is a single
symbol for the result
• Step 3: If so, write it and go to the next
column. If not, write the accompanying
number and carry the appropriate value to
the next column
Subtraction Rules
• Step1: Start with the rightmost column, if the
column of the minuend is greater than that of the
subtrahend, do the subtraction, if not…
• Step 2: Borrow one unit from the digit to the left
of the once being processed
– The borrowed unit is equal to “borrowing” the radix
• Step 4: Decrease the column form which you
borrowed by one
• Step 3: Subtract the subtrahend from the minuend
and go to the next column
Addition of Binary Numbers
• Rules for adding or subtracting very similar
to the ones in decimal system
– Limited to only two digits
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•
•
•
0+0=0
0+1=1
1+0=1
1 + 1 = 0 carry 1
Addition & Subtraction of Hex
• Due to the propensity for errors in binary, it
is preferable to carry out arithmetic in
hexadecimal and convert back to binary
• If we need to borrow in hex, we borrow 16
• It is convenient to think “in decimal” and
then translate the results back to hex
Representing No.s in a Computer
• Remember, all numeric data is represented inside
the computer as 1s and 0s
– Arithmetic operations, particularly subtraction raise the
possibility that the result might be negative
• Any numerical convention needs to differentiate
two basic elements of any given number, its sign
and its magnitude
– Conventions
• Sign-magnitude
• Two’s complement
• One’s complement
Representing Negatives
• It is necessary to choose one of the bits of the
“basic unit” as a sign bit
– Usually the leftmost bit
– By convention, 0 is positive and 1 is negative
• Positive values have the same representation in all
conventions
• However, in order to interpret the content of any
memory location correctly, it necessary to know
the convention being used used for negative
numbers
Comparing the Conventions
Bit Pattern
000
001
010
011
100
101
110
111
Unsigned
0
1
2
3
4
5
6
7
Sign1's
2's
Magnitude Complement Complement
0
0
0
1
1
1
2
2
2
3
3
3
-0
-3
-4
-1
-2
-3
-2
-1
-2
-3
-0
-1
Sign-Magnitude
• For a basic unit of N bits, the leftmost bit is
used exclusively to represent the sign
• The remaining (N-1) bits are used for the
magnitude
• The range of number represented in this
convention is –2 N+1 to +2 N-1 -1
Sign-magnitude Operations
• Addition of two numbers in sign-magnitude is
carried out using the usual conventions of binary
arithmetic
– If both numbers are the same sign, we add their
magnitude and copy the same sign
– If different, determine which number I
– has the larger magnitude and subtract the other from it.
The sign of the result is the sign of the operand with the
larger magnitude
– If the result is outside the bounds of –2 n+1 to +2 n-1 –1,
an overflow results
Two’s Complement Convention
•
•
A positive number is represented using a
procedure similar to sign-magnitude
To express a negative number
1.
2.
3.
–
–
Express the absolute value of the number in binary
Change all the zeros to ones and all the ones to zeros (called
“complementing the bits”)
Add one to the number obtained in Step 2
The range of negative numbers is one larger than
the range of positive numbers
Given a negative number, to find its positive
counterpart, use steps 2 & 3 above
Two’s Complement Operations
• Addition:
– Treat the numbers as unsigned integers
• The sign bit is treated as any other number
– Ignore any carry on the leftmost position
• Subtraction
– Treat the numbers as unsigned integers
– If a borrow is necessary in the leftmost place,
borrow as if there were another “invisible” onebit to the left of the minuend
Overflows in Two’s Complement
• The s range of values in two’s-complement
is –2 n+1 to +2 n-1 –1
• Results outside this band are overflows
• In all overflow conditions, the sign of the
result of the operation is different than that
of the operands
• If the operands are positive, the result is negative
• If the operands are negative, the result is positive
One’s Complement
• Devised to make the addition of two numbers with
different signs the same as two numbers with the
same sign
• Positive numbers are represented in the usual way
• For negatives
– STEP 1: Start with the binary representation of the
absolute value
– STEP 2: Complement all of its bits
• Operations
– Treat the sign bit as any other bit
– For addition, carry out of the leftmost bit is added to the
rightmost bit – end-around carry
Binary & Alphanumeric Codes
• A binary code is a group of n bits that
assume up to 2n distinct combinations of 1’s
and 0’s with each combination representing
one element of the set that is being coded
• With two bits we can form a set of four elements
• With three bits we can represent 8 elements
• With four bits we can represent 16 elements
Weighted Codes
• A sequence of binary digits representing a decimal
digit is called a code word
– The code with weights 8, 4, 2, 1 is know as the BinaryCoded-Decimal (BDC) code
– Another code could be weighted 2-4-1-2
• Some codes are not unique in representing
decimal numbers
– These codes cannot be used interchangeably
– The correct code is self-complementing
• The value of 9-N can be obtained by complementing the bits of
the code
Alphanumeric Codes
• American Standard Code for Information
Interchange (ASCII)
– 7-bit code
– Since the unit of storage is a bit, all ASCII codes are
represented by 8 bits, with a zero in the most significant
digit
– H e l l o W o r l d
– 48 65 6C 6C 6F 20 57 6F 72 6C 64
• Extended Binary Coded Decimal Interchange
Code (EBCDIC)
Error Detection
– When binary data is transmitted, there is a possibility of
– an error in transmission due to equipment failure or
noise
• Bits change from 0 to 1 or vice-versa
– The number of bits that have to change within a byte
before it becomes invalid characterizes the code
• Single-error-detecting code
– To detect single errors have occurred we use an added parity
check bit – makes each byte either even or odd
• Two-error-detecting code
– The minimum distance of a code is the number of bits
that need to change in a code word to result another
valid code word
– Some codes are self-correcting (error-correcting code)
Even Parity Example
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•
•
•
•
•
Bytes Transmitted
11100011
11100001
01110100
11110011
10000101 Parity Block
B
I
T
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•
•
•
•
•
Bytes Received
11100011
11100001
01111100
11110011
10000101 Parity Block
B
I
T
Hamming Code
• This method of multiple-parity checking
can be used to provide multiple-error
detection