j. michael moore computer organization csce 110. j. michael moore high level view of a computer...
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J. Michael Moore
Computer Organization
CSCE 110
J. Michael Moore
High Level View Of A Computer
ProcessorInput Output
Memory
Storage
J. Michael Moore
Getting Data In
Input
Others?
J. Michael Moore
ProcessorInput Output
Memory
Storage
J. Michael Moore
Getting Data Out
Output
Others?
J. Michael Moore
ProcessorInput Output
Memory
Storage
J. Michael Moore
Unit of Storage
• Bit–Binary digit
– Smallest unitof measurement
Memory
Storage
Two possiblevalues
on offOR
J. Michael Moore
How Data Is Stored
• Byte: a group of 8 bits; 28=256 possibilities– 00000000, 00000001, 00000010, 00000011,
… , 11111111
• Memory: long sequence of locations, each large enough to hold one byte, numbered 0, 1, 2, 3, …
• Address: The number of the location
J. Michael Moore
How Data Is Stored
• Contents of a location can change– e.g. 01011010 can become 11100001
• Use consecutive locations to store longer sequences– e.g. 4 bytes = 1 word
1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 00
3...
bytes
0 1 2
bits
J. Michael Moore
Binary Numbers
• Base Ten Numbers (Integers)– characters
• 0 1 2 3 4 5 6 7 8 9
– 5401 is 5x103 + 4x102 + 0x101 + 1x100
• Binary numbers are the same– characters
• 0 1
– 1011 is 1x23 + 0x22 + 1x21 + 1x20
J. Michael Moore
Converting Binary to Base 10
• 23 = 8
• 22 = 4
• 21 = 2
• 20 = 1
1. 10012 = ____10 =
2. 1x23 + 0x22 + 0x21+ 1x20 =
3. 1x8 + 0x4 + 0x2 + 1x1 =
4. 8 + 0 + 0 + 1 =
5. 910
• 01102 = ____10 (Try yourself)
• 01102 = 610
J. Michael Moore
Converting Base 10 to Binary
• 28 = 256• 27 = 128• 26 = 64• 25 = 32• 24 = 16• 23 = 8• 22 = 4• 21 = 2• 20 = 1
• 38810 = ____2
28 27 26 2425 2223 2021
1 1 10 00 0 00
• 388 - 256 (28) = 132
• 132 - 128 (27) = 4
• 4 - 4 (22) = 0
J. Michael Moore
Converting Base 10 to Binary• 38810 = ____2 • 38810 / 2 = 19410 Remainder 0• 19410 / 2 = 9710 Remainder 0• 9710 / 2 = 4810 Remainder 1• 4810 / 2 = 2410 Remainder 0• 2410 / 2 = 1210 Remainder 0• 1210 / 2 = 610 Remainder 0• 610 / 2 = 310 Remainder 0• 310 / 2 = 110 Remainder 1• 110 / 2 = 010 Remainder 1
28 27 26 2425 2223 2021
1 1 10 00 0 00
J. Michael Moore
Other common number representations
• Octal Numbers– characters
• 0 1 2 3 4 5 6 7 8
– 7820 is 7x83 + 8x82 + 2x81 + 0x80
• Hexadecimal Numbers– characters
• 0 1 2 3 4 5 6 7 8 9 A B C D E F
– 2FD6 is 2x163 + Fx162 + Dx161 + 6x160
http://fac-staff.seattleu.edu/quinnm/web/education/JavaApplets/applets/NumConv.html
J. Michael Moore
Negative Numbers
• Can we store a negative sign?
• What can we do?– Use a bit
• Most common is two’s complement
J. Michael Moore
Representing Negative Numbers
• Two’s Complement– flip all the bits
• change 0 to 1 and 1 to zero
– add 1– if the leftmost bit is 0, the number is 0 or
positive– if the leftmost bit is 1, the number is negative
J. Michael Moore
Two’s Complement
• What is -9?– 9 is 00001001 in binary– flip the bits - 11110110– add 1 - 11110111
• Addition and Subtraction are easy– always addition
J. Michael Moore
Two’s Complement
• Addition– 13 - 9 = 4– 13 + (-9) = 4– 00001101 + 11110111 = ?
0
0 100 0 0 11
1
1
0
1
01 1 1 11 1 1
1
0
11 1 1
0000 4=
1
This bit is lost
But that doesn’t matter since we get the
correct answer anyway
J. Michael Moore
Real (Floating point) numbers
• Break the bits used into parts
0110101000000011
Mantissa Exponent
Sign bits
J. Michael Moore
Limitations of Finite Data Encodings
• Overflow - number is too large– suppose 1 byte stores integers in base 2,
from 0 (00000000) to 255 (11111111) (note: this is not two’s complement although it would have the same problem)
– if the byte holds 255, then adding 1 to it results in 0, not 256
– http://www.artima.com/insidejvm/applets/InnerInt.html– http://classes.engr.oregonstate.edu/eecs/fall2007/cs160/applets/
TwosComplement.html
J. Michael Moore
Limitations of Finite Data Exchange
• Roundoff Error– Insufficient precision (size of word)
• ex. Try to store 1/8, which is 0.001 in binary, with only two bits
– Nonterminating expansions in current base• ex. Try to store 1/3 in base 10, which is 0.3333…
– Nonterminating expansions in every base• ex. Irrational numbers such as
J. Michael Moore
ProcessorInput Output
Memory
Storage