Transcript instructions per second

Introduction to Computing
Lecture # 7
Outline
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Number Systems
Binary Numbers
Boolean Logic & Truth Tables
Processing hardware
How processor works
Von Neumann Architecture
Number Systems
• In all positional number systems
– The value of the base determines the total number
of different symbols or digits available in the
number system. The first of these choices is
always zero.
– The maximum value of a single digit is always
equal to one less than the value of the base.
• Decimal Number System
– Base is equal to 10 (ten symbols or digits)
– The successive positions to the left of the decimal
point represent units, tens, hundreds, thousands,
etc.
– Example: 2586 (2*1000 + 5*100 + 8*10 + 6*1)
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Number Systems
• Octal Number System
– Base is equal to 8 (eight symbols or digits)
– Each position in an octal number represents a
power of the base (8).
– Example: 20578 (2*83 + 0*82 + 5*81 + 7*80) =
107110
• Hexadecimal Number System
– Base is equal to 16 (sixteen symbols or digits)
– 0, 1, 2, … , 9, A, B, C, D, E, F
– Each position in an hexadecimal number
represents a power of the base (16).
– Example: 1AF16 (1*162 + 10*161 + 15*160) = 43110
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Number Systems
• Binary Number System
– Base is equal to 2 (two symbols or digits)
– 0 and 1
– Each position in a binary number represents a
power of the base (2).
– Example: 101012 ( 1*24 + 0*23 + 1*22 + 0*21 + 1*20)
= 2110
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The Binary System
Calculation in computer uses binary system
(consisting of 1 or 0, represented by On/Off electrical
States respectively )
• The binary system has only two digits: 0 and 1
• Each 0 or 1 is called a bit (binary digit)
• Bits can be used to represent:
– Numbers
– Characters
– Commands / Programs
– Image / Picture (Bitmap)
– Voice / Music…etc
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Binary Bits as Characters
• How to represent character using 0/1 ?
• By grouping multiple 0 & 1s together
• For example:
– by grouping 2 bits,
4 patterns are formed:
00, 01, 10, 11
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• By grouping eight 0 & 1,
28 = 256 patterns can be
formed and we could assign
each pattern to different
characters
• In computer, character is
represented by 8 bits
• A group of 8 bits is called byte
Binary Bits as Characters
• Byte is a small unit. For convenience, some larger
units are defined as follows:
• Kilobyte (KB)
1024 bytes (210 = 1024)
– 1 KB equals about one-half page of text
• Megabyte (MB) 1,048,576 bytes (one million approx.)
– 1 MB equals about 500 pages of text
• Gigabyte (GB) 1,073,741,824 bytes (one billion approx.)
– 1 GB equals about 500,000 pages of text
• Terabyte (TB) 1,009,511,627,776 (1 trillion bytes
approx.)
– 1 TB equals about 500,000,000 pages of text
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• Petabyte (PB) 1,048,576 gigabytes (1 quadrillion
bytes approx)
Binary Bits as Characters
 The prefix “mega” in “megabyte” comes from the
Greek word “megas” meaning “mighty” or “great.”
 The prefix “giga” in “gigabyte” comes from a Greek
word meaning “giant.”
 The prefix “tera” in “terabyte” comes from a Greek
word meaning “monster.”
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 You might think that the largest unit of storage
capacity is a petabyte, but in fact, there are also
exabytes, zetabytes, and yottabytes.
Binary Bits as Characters
How to map a group of 8 bits to a single
ASCII (American
character?
Standard Code for
Information Interchange)the binary code most
widely used with
microcomputers
EBCDIC (Extended
Binary Coded Decimal
Interchange Code) - used
with large computers,
such as mainframes.
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Unicode - uses two bytes
for each character rather
than one (65,536
character combinations).
Binary Bits as Characters
• ASCII has 256 patterns and is good enough to store
a-z, A-Z, 0-9 and punctuations.
• How about other characters ?
(Chinese has more than 40 thousands
characters/symbols…)
• New standard to store international/Asian characters
is Unicode
• Unicode encode a character with 16 bits (216 =
65536), which is large enough for Chinese and other
character sets such as Japanese, Korean, Thai..etc
• Newest version is Unicode 6.0 dated 04-OCT-2011.
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Boolean Logic & Truth Tables
• Logical Addition
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– The symbol + is used for
logical addition
– Also known as OR
operator
– We can define the OR
operator by listing all
possible combinations of
A and B, and the resulting
value of C, in the
equation A+B=C
– Since A and B can have
only two possible values
(0 or 1), only four
combinations of input are
possible
A
B
C=A+B
0
0
0
0
1
1
1
0
1
1
1
1
Truth Table for logical OR
Boolean Logic & Truth Tables
• Logical Multiplication
– The symbol . is used for
logical multiplication
– Also known as AND
operator
– We can define the AND
operator by listing all
possible combinations of
A and B, and the resulting
value of C, in the
equation A.B=C
– Since A and B can have
only two possible values
(0 or 1), only four
combinations of input are
possible
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A
B
C=A.B
0
0
0
0
1
0
1
0
0
1
1
1
Truth Table for logical AND
Boolean Logic & Truth Tables
• Complementation
– The symbol - is used for
complementation
– Also known as NOT
operator
– Unary operator
– Ā means complement of
A or NOT of A
– The complementation of
a variable is the reverse
of its value.
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A
Ā
0
1
1
0
Truth Table for logical NOT
Binary Bits as Program: Machine Language
• Binary bits sequence are also used as “commands” /
“programs” to tell CPU what to do.
• Machine language - a binary-type programming
language that the computer can run directly.
• (e.g. 01010000 00000001 00000000)
• Machine language is difficult to write and maintain,
hence Assembly language (Human readable
instructions) are used instead. (e.g. ADD AX,1)
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Binary Bits as Program: Machine Language
• Assembly language instructions used in different
processors are different.
• Meanwhile the architectures of micro-processors can
be classified into two major types
• CISC (Complex Instruction Set Computing)
– Supports a large number of instructions at relatively low
processing speeds (used mostly in PCs and mainframes)
– e.g. Intel Pentium, Motorola 68K CPU
– Instruction (Command) more comprehensive
– Program tends to be shorter
• RISC (Reduced Instruction Set Computing)
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– Supports a reduced number of instructions in order to obtain
faster processing speeds (used mostly in workstations)
– e.g. PowerPC (Apple), ARM process (Game Boy Advance)
– Instruction more compact/simple
– Overall performance more efficient than CISC
• End of Today Lecture
• Questions ?
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The Motherboard
• Motherboard - the
main circuit board in the
system unit
• Expansion – increasing
a computer’s
capabilities by adding
hardware
• Upgrading – changing
to newer, more powerful
versions
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The Microprocessor Chip
• Two kinds of microprocessors used in most
personal computers today:
• Intel-type chips made by Intel, Advance
Micro Devices (AMD), Cyrix, DEC, and others.
These are used by manufacturers such as
Compaq, Dell, Gateway, Hewlett-Packard,
and IBM.
• Motorola-type chips made by Motorola for
Apple Macintosh computers.
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The Microprocessor Chip
 System clock – controls how fast all the operations
within a computer take place.
 The system clock uses fixed vibrations from a quartz
crystal to deliver a steady stream of digital pulses or
ticks to the CPU.
 These ticks are called cycles. Faster clock speeds will
result in faster processing and execution.
 There are 4 ways in which processing speeds are
measured.
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The Microprocessor Chip
1. For microcomputers – megahertz and
gigahertz
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
Megahertz (MHz) - a measure of frequency
equivalent to 1 million cycles (ticks of the system
clock) per second.
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Gigahertz (GHz) - a measure of frequency
equivalent to 1 billion cycles per second.
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Example: the Pentium 4, operates at 1.4 gigahertz
and it has 42 million transistors.
The Microprocessor Chip
2. For workstations and mainframes – MIPS
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
Measuring the speed in terms of number of
instructions per second that a computer can
process.
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MIPS - millions of instructions per second.
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High-end microcomputer or workstation – 100 MIPS
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Mainframe – 200-1200 MIPS
The Microprocessor Chip
3. For supercomputers – flops
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
Flops - floating-point operations per second.
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Megaflop - one million flops.
Gigaflop - one billion flops.
Teraflop - one trillion flops.
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U.S. supercomputer known as “Option Red” – 1.34
teraflops
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IBM’s supercomputer “Blue Gene” – 1 petaflop
The Microprocessor Chip
4. For all computers – fractions of a second
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
Millisecond - one-thousandth of a second.
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Microsecond - one-millionth of a second.
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Nanosecond - one-billionth of a second.
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Picosecond - one-trillionth of a second.
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Microcomputers – microseconds

Supercomputers – nanoseconds or picoseconds
The Microprocessor Chip
Microcomputers
Megahertz
& Gigahertz
Workstation
Mainframes
s
X
X
MIPS
X
X
FLOPS
Fractions of
a second
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Supercomputers
X
X
X
X
How the Processor or CPU works:
Control Unit, ALU, & Registers
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How the Processor or CPU works:
Control Unit, ALU, & Registers
 Word size - the number of bits that the
processor may process at any one time. The
larger the word size, the faster the computer.
 Example:
 A 32-bit computer (one with 32-bit-word processor)
will transfer data within each microprocessor chip
in 32-bit chunks or 4 bytes at a time.
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How the Processor or CPU works:
Control Unit, ALU, & Registers

The CPU is the brain of the computer; it
follows the instructions of the software to
manipulate data into information.

The CPU consists of two parts: the control
unit and the arithmetic logic unit, both of
which contain registers, or high speed
storage areas.

All are linked by a kind of electronic roadway
called a bus.
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How the Processor or CPU works:
Control Unit, ALU, & Registers
 The control unit
 Deciphers each instruction stored in it and then carries
out the instruction.
 Directs electronic signals between memory and ALU
and also between memory and I/O devices.
 The arithmetic/logic unit
 The ALU performs arithmetic and logical operations.
 Machine Cycle – Consists of four basic operations for
every instruction.
 Fetch an instruction
 Decode an instruction
 Execute the instruction
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 Stores the result
How the Processor or CPU works:
Control Unit, ALU, & Registers
Machine cycle
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How the Processor or CPU works:
Control Unit, ALU, & Registers
 Registers
 Special high speed storage areas that temporarily
store data during processing.
 Stores instruction, data, results.
 Example: instruction register, address register,
storage register, and accumulator register.
 Buses
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 Electrical data roadways through which bits are
transmitted within the CPU and between the CPU
and other components of the motherboard.
 Resembles a multilane highway – more lanes it
has, faster the bits can be transferred.
Von Neumann Architecture
• The von Neumann architecture is a computer design
model that uses a processing unit and a single
separate storage structure to hold both instructions
and data.
• It is named after mathematician and early computer
scientist John von Neumann.
• The term "von Neumann architecture" arose from
mathematician John von Neumann's paper, “First
Draft of a Report on the EDVAC” Dated June 30,
1945
• The term "stored-program computer" is generally
used to mean a computer of this design, although as
modern computers are usually of this type, the term
has fallen into disuse.
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Von Neumann Architecture
Memory
Control Unit
Arithmetic and Logic Unit
Accumulator
Input
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Output
Von Neumann Bottleneck
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• The separation between the CPU and memory leads
to the von Neumann bottleneck, the limited
throughput (data transfer rate) between the CPU and
memory compared to the amount of memory.
• In modern machines, throughput is much smaller than
the rate at which the CPU can work.
• This seriously limits the effective processing speed
when the CPU is required to perform minimal
processing on large amounts of data.
• The CPU is continuously forced to wait for vital data to
be transferred to or from memory.
• As CPU speed and memory size have increased
much faster than the throughput between them, the
bottleneck has become more of a problem.
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