Download Computer Organization Lecture 2 Section 1.2 Robb T. Koether

Computer Organization
Lecture 2
Section 1.2
Robb T. Koether
Hampden-Sydney College
Fri, Aug 30, 2013
Robb T. Koether (Hampden-Sydney College)
Computer Organization
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1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
Robb T. Koether (Hampden-Sydney College)
Computer Organization
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
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The Main Components
The Central Processing Unit (CPU)
Memory
Input devices
Output devices
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The CPU
The central processing unit (CPU).
The register bank.
The arithmetic and logic unit (ALU).
The branch unit.
The memory read/write unit.
The control unit.
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The CPU
The CPU:
Performs arithmetic.
Addition, subtraction, logical operations, etc.
Makes logical decisions.
Branch if two values are equal, etc.
Loads data from memory to registers.
Stores data from registers to memory.
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Memory
Levels of memory.
Registers (in the CPU).
Level 1 Cache (L1)
Holds commonly used data.
“10% of the data is used 90% of the time.”
Level 2 Cache (L2)
Holds less commonly used data.
Main Memory
Holds data that are “seldom” used.
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
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Representing Data
How can a machine “store” a number?
We design a machine that can be put into different “states.”
Each state represents a value.
For example, the values 0 through 9 may be represented by 10
different states.
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Representation of Data
How could we represent the values 0 through 99?
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Representation of Data
How could we represent the values 0 through 99?
Build a machine with 100 states.
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Representation of Data
How could we represent the values 0 through 99?
Build a machine with 100 states.
Or, build two machines with 10 states each.
One machine represents the 1’s digit.
The other machine represents the 10’s digit.
With six 10-state machines, we could represent values from 0 to
999999.
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Binary Representation of Data
In computers, it is more efficient to use only two states.
A light: on/off
A switch: open/closed
Voltage: high/low
Therefore, numbers will be stored in binary rather than decimal.
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
Robb T. Koether (Hampden-Sydney College)
Computer Organization
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Binary Representation of Data
With 1 bit, we can represent 2 different values, namely 0 and 1.
With 2 bits, we can represent 4 different values, namely 0 through
3.
Pattern
00
01
10
11
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Value
0
1
2
3
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Binary Representation of Data
With 3 bits, we can represent 8 values, namely 0 through 7.
Pattern
000
001
010
011
100
101
110
111
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Value
0
1
2
3
4
5
6
7
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Negative Numbers
If we wanted to represent negative numbers using 2 bits, we could
represent −2 through +1.
Pattern
00
01
10
11
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Value
0
1
−2
−1
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Negative Numbers
With 3 bits, we can represent −4 through +3.
Pattern
000
001
010
011
100
101
110
111
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Value
0
1
2
3
−4
−3
−2
−1
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Fixed-Length Binary Numbers
In general, n bits can represent any of 2n different values, ranging
from 0 to 2n − 1.
4 bits represent values from 0 to 15.
8 bits represent values from 0 to 255.
16 bits represent values from 0 to 65535, etc.
Or we can represent signed numbers from −2n−1 to 2n−1 − 1.
16 bits represent values −32768 to +32767.
32 bits represent values −2147483648 to +2147483647.
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Binary Number System
In the binary number system, each position in the number
represents a power of 2.
Example: 101011 represents
(1 × 25 ) + (0 × 24 ) + (1 × 23 ) + (0 × 22 ) + (1 × 21 ) + (1 × 20 )
which equals 32 + 8 + 2 + 1 = 43.
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The Structure of Memory
1 bit = 1 binary digit (0 or 1).
1 half-byte (nibble) = 4 bits.
1 byte = 2 nibbles = 8 bits.
1 half-word = 2 bytes = 16 bits.
1 word = 4 bytes = 32 bits (standard size).
1 kilobyte (Kb) = 1024 bytes = 210 bytes.
1 megabyte (Mb) = 1024 K = 220 bytes.
1 gigabyte (Gb) = 1024 M = 230 bytes.
1 terabyte (Tb) = 1024 T = 240 bytes.
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
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Computer Organization
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Hexadecimal Numbers
For convenience, we often display values in hexadecimal (base
16).
The hexadecimal system has 16 digits with values 0 through 15.
Digit
0
1
2
3
4
5
6
7
Robb T. Koether (Hampden-Sydney College)
Value
0
1
2
3
4
5
6
7
Digit
8
9
A
B
C
D
E
F
Computer Organization
Value
8
9
10
11
12
13
14
15
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Examples of Hexadecimal Numbers
4A16 = (4 × 16) + 10 = 74,
FF16 = (15 × 16) + 15 = 255,
12316 = (1 × 162 ) + (2 × 16) + 3 = 292,
FACE16 = (15 × 163 ) + (10 × 162 ) + (12 × 16) + 14
= 61440 + 2560 + 192 + 14
= 64206.
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Hexadecimal Numbers
Hexadecimal numbers are convenient because
They are compact.
There is a very simple relation between them and binary numbers.
One hexadecimal digit represents a 4-digit binary number (values 0
- 15), or half a byte.
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
Robb T. Koether (Hampden-Sydney College)
Computer Organization
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Conversion from Hexadecimal to Binary
Convert 2B6F to binary
Write each hex digit as a 4-bit binary number.
2 = 0010
B = 1011
6 = 0110
F = 1111
Write the 4-bit numbers together as a single binary number
0010101101101111
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Conversion from Binary to Hexadecimal
Convert 1001101011101011 to hexadecimal.
Break it up into groups of 4 bits (starting on the right).
1001 1010 1110 1011
Write each block of 4 bits as a hex digit.
9
A
E
B
Write the hex digits as a single hex number.
9AEB
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Outline
1
The Main Components
2
Storing Numbers
Binary Numbers
Hexadecimal Numbers
Converting Between Binary and Hexadecimal
3
Assignment
Robb T. Koether (Hampden-Sydney College)
Computer Organization
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Assignment
Homework
Read Sections 1.2.
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