J. Michael Moore

Computer Organization

CPSC 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

• ___–___________

– Smallest unitof measurement

Memory

Storage

Two possiblevalues

on offOR

J. Michael Moore

How Data Is Stored

• ___: a group of 8 bits; 28=256 possibilities– 00000000, 00000001, 00000010, 00000011,

… , 11111111

• ___________: long sequence of locations, each large enough to hold one byte, numbered 0, 1, 2, 3, …

• ___________: 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

• _____________ Numbers– characters

• 0 1 2 3 4 5 6 7 8

– 7820 is 7x83 + 8x82 + 2x81 + 0x80

• _____________ Numbers– characters

• 0 1 2 3 4 5 6 7 8 9 A B C D E F

– 2FD6 is 2x163 + Fx162 + Dx161 + 6x160

J. Michael Moore

__________ Numbers

• Can we store a __________ sign?

• What can we do?– Use a ____

• Most common is ____________________

J. Michael Moore

Representing ________ Numbers

• ____________________________– flip all the bits

• change 0 to 1 and 1 to zero

– add 1– if the leftmost bit is __, the number is __ or

_______________– if the leftmost bit is __, the number is

_______________

J. Michael Moore

______________________

• 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

_______________________

• 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 (____________) numbers

• Break the bits used into parts

0110101000000011

________ ________

Sign bits

J. Michael Moore

Limitations of Finite Data Encodings

• __________ - number is too large– suppose 1 byte stores integers in base 2,

from 0 (00000000) to 255 (11111111) (note: this is not ___________________ although it would have the same problem)

– if the byte holds 255, then adding 1 to it results in __, not _____

J. Michael Moore

Limitations of Finite Data Exchange

• ___________ Error– Insufficient ___________ (size of word)

• ex. Try to store 1/8, which is 0.001 in binary, with only two bits

– ______________ expansions in current base• ex. Try to store 1/3 in base 10, which is 0.3333…

– ______________ expansions in every base• ex. Irrational numbers such as

J. Michael Moore

ProcessorInput Output

Memory

Storage