1. Computer Organization
CSCE 110
J. Michael Moore

2. High Level View Of A Computer
Memory
Input
Processor
Output
Storage
J. Michael Moore

3. Getting Data In
Input
Others?
J. Michael Moore

4. Memory
Input
Processor
Output
Storage
J. Michael Moore

5. Getting Data Out
Output
Others?
J. Michael Moore

6. Memory
Input
Processor
Output
Storage
J. Michael Moore

7. Unit of Storage Bit Two possible values OR Binary digit
Memory
Bit
Binary digit
Smallest unit of measurement
Two possible
values
off OR on
Storage
J. Michael Moore

8. How Data Is Stored Byte: a group of 8 bits; 28=256 possibilities
, , , , … ,
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

9. How Data Is Stored Contents of a location can change
bits 1 1 2
3...
bytes
Contents of a location can change
e.g can become
Use consecutive locations to store longer sequences
e.g. 4 bytes = 1 word
J. Michael Moore

10. Binary Numbers Base Ten Numbers (Integers) Binary numbers are the same
characters
5401 is 5x x x x100
Binary numbers are the same
0 1
1011 is 1x23 + 0x22 + 1x21 + 1x20
J. Michael Moore

11. Converting Binary to Base 10
23 = 8
22 = 4
21 = 2
20 = 1
10012 = ____10 =
1x23 + 0x22 + 0x21+ 1x20 =
1x8 + 0x4 + 0x2 + 1x1 = =
910
01102 = ____10 (Try yourself)
01102 = 610
J. Michael Moore

12. 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) = 132
(27) = 4
4 - 4 (22) = 0 28 27 26 24 25 22 23 20 21 1 1 1
J. Michael Moore

13. Converting Base 10 to Binary
38810 = ____2
38810 / 2 = 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 28 27 26 24 25 22 23 20 21
110 / 2 = 010 Remainder 1 1 1 1
J. Michael Moore

14. Other common number representations
Octal Numbers
characters
7820 is 7x83 + 8x82 + 2x81 + 0x80
Hexadecimal Numbers
A B C D E F
2FD6 is 2x163 + Fx162 + Dx x160
J. Michael Moore

15. Negative Numbers Can we store a negative sign? What can we do?
Use a bit
Most common is two’s complement
J. Michael Moore

16. 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

17. Two’s Complement What is -9? Addition and Subtraction are easy
9 is in binary
flip the bits
add
Addition and Subtraction are easy
always addition
J. Michael Moore

18. Two’s Complement 1 1 1 = 4 Addition 13 - 9 = 4 13 + (-9) = 4
= ?
But that doesn’t
matter since
we get the
correct answer
anyway 1 1 1 1 1 1 1 1 1 1
This bit is lost 1 = 4
J. Michael Moore

19. Real (Floating point) numbers
Break the bits used into parts
Sign bits
Mantissa
Exponent
J. Michael Moore

20. Limitations of Finite Data Encodings
Overflow - number is too large
suppose 1 byte stores integers in base 2, from 0 ( ) to 255 ( ) (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
J. Michael Moore

21. Limitations of Finite Data Exchange
Roundoff Error
Insufficient precision (size of word)
ex. Try to store 1/8, which is in binary, with only two bits
Nonterminating expansions in current base
ex. Try to store 1/3 in base 10, which is …
Nonterminating expansions in every base
ex. Irrational numbers such as 
J. Michael Moore

22. Memory
Input
Processor
Output
Storage
J. Michael Moore