1. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU1 Course Overview First Material

2. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU2 Class 1 outline  Course Syllabus  Information Representation  Number Systems  Material from sections 1-1 and 1-2 of text  Personal course website ece.osu.edu/~degroat

3. Information Representation  In the real world Items that we want to measure are continuous, i.e., they can have any value  Weight  Temperature  Pressure  Velocity  And many, many others 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU3

4. But in a computer  The paradigm of a computer that we are familiar with is electronic. But there have been others like Babbage’s compute engine and cash registers which were mechanical.  The electronics make it easy to represent two states, on and off, or high voltage level and low voltage level. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU4

5. Realization  Result: representation of real world quantities by a system that can only represent discrete states, and thus discrete quantities.  Example Use you fingers to represent temperature from 10 o F to 100 o F. What values did you represent? 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU5

6. Realization  Result: representation of real world quantities by a system that can only represent discrete states, and thus discrete quantities.  Example Use you fingers to represent temperature from 10 o F to 100 o F. What values did you represent? Ans: partially depends on whether it was in 8 or 10 steps. So it was either in 10 o F steps or 12.5 o F steps. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU6

7. Digital Systems  Digital electronics have progressed from 12V logic elements to 1.2V logic elements. Could use these values OR Use a representation of 1 for a HIGH And a representation of 0 for a LOW  In electronics we restrict ourselves to just these two states to provide interpretation of a range of voltages as HIGH or a 1 and another range as LOW or a 0. Why? 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU7

8. The Digital Computer  “Virtually every aspect of digital system design is encompassed in a computer design” (Hill and Peterson)  “Computers are the most important type of digital sytem”  Computers and digital systems have become pervasive in our world From cell phones to MP3 players to …… 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU8

9. Computers & digital systems today  There everywhere, there everywhere PCs and Workstations Cell phones MP3 players Cameras Your automobile – an automobile will have 15 to 40 embedded processors Microwaves Stoves, Dishwashers, fautces (auto temp control) Washers, Dryers, Vacuum cleaners And on and on and on and on and …………. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU9

10. The computer  Major components The CPU – central processing unit – the datapath combined with the control unit  Datapath – performs the actual arithmetic and logic functions on the data  Control Unit – THE BRAIN – controls the flow of data and instructions, decoding and executing instructions MEMORY – Consists of both registers, main memory and secondary memory I/O or Input/Output – communication channels to get information into and out of the computer 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU10

11. Computers and digital systems  Each of the components of “The Computer” is a digital component  “The computer” consists of an interconnected set of digital modules.  Most of the components is are designed with not much more than the techniques of this class. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU11

12. Number Systems  In digital systems you can only represent 2 states.  A base 10 number systems is simply not straightforward.  Will need a different number system.  Concepts across number systems are the same. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU12

13. General number systems  A number system has a base or radix, r  A number in base r contains digits 0,1,2,…,r-1  The value represented as a power series in r as A n-1 r n-1 + A n-2 r n-2 + … + A 1 r 1 + A 0 r 0 + A -1 r -1 + A -2 r -2 + … + A -m r -m  and is written  A n-1 A n-2 …A 1 A 0. A -1 A -2 …A -m 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU13

14. General number systems (2)  The “. “ is called the radix point. In base 10 it is the decimal point In base 2 it is the binary point  is referred to as the most significant digit Referred to as the msb  is referred to as the least significant digit Referred to as the lsb Usually m=0 so is the lsb 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU14

15. For base 10 or radix 10  Example - book 724.5  421 From prior education may have referred to digits as the units, tens and hundred positions  421 = 4.21 x 10 2 in scientific notation  421 = 4 x 10 2 + 2 x 10 1 + 1 x 10 0 (Recalling that anything to the 0 power is 1) 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU15

16. Something in base or radix 5  (123) 5 What is it’s value? (Note method of showing base of number)  Value Val (123) 5 = 1 x 5 2 + 2 x 5 1 + 3 x 5 0 = 25 + 10 + 3 = (38) 10 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU16

17. Binary numbers – base or radix 2  Have binary digits 0 and 1  So all number represented in binary have only digits 0 and 1  11010 would have value? = 1 x 2 4 + 1 x 2 3 + 0 x 2 2 + 1 x 2 1 + 0 x 2 0 + = 1 x 16 + 1 x 8 + 0 x 4 + 1 x 2 + 0 x 1 = 16+8+2 = (26) 10 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU17

18. Know the powers of two  The first 16 powers of two are in the following table. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU18 n2^n n2^N 01 8256 12 9512 24 101024 38 112048 416 124096 532 138192 664 1416384 7128 1532768

19. Some common size terms  2 10 is commonly referred to as kilo or K  2 20 is commonly referred to as mega or M  2 30 is commonly referred to as giga or G  2 40 is commonly referred to as tera or T  So 4K is = 2 2 x 2 10 = 2 12 = 4096 10 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU19

20. Base 10 to binary  One method Subtract the largest power of two from the value and repeat until done. Text example 652 146  Largest if 128 or 2 7 leaving18  Then have 16 or 2 4 leaving just 2  Which is 2 1 giving value  1 0 0 1 0 0 1 0 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU20

21. Fractional Parts  In base 10 Have xx.12 which is 1 x 10 -1 + 2 x 10 -2  In base 2 Have binary point xxx.1 which is 1 x 2 -1 or 0.5 (1/2) And xxx.01 which is 1 x 2 -2 or 0.25 (1/4) And xxx.001 which is 1 x 2 -3 or 0.125 (1/8) And xxx.0001 which is 1 x 2 -4 or 0.0625 (1/16) 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU21

22. In digital systems and computer  Have two other radix systems that are related to binary or base 2 as they are powers of it.  Octal or base 8 Can get an octal representation by grouping a binary number into groups of 3 digits. Octal numbers use 8 distinct digits 0 through 7 110010 = 110 010 = (6 2) 8 for example And can use same general number systems expansion shown earlier. 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU22

23. Hex  Hex or Hexadecimal is more common than Octal representation today  Hex is base or radix 16  Thus group 4 binary digits  1111 0100 1011 would be? F 4 B  For representation need 16 symbols Use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU23

24. Class 1 assignment  Read sections 1-1 and 1-2  Problems for hand in 1-4, 1-8, 1-9  Problems for practice 1-10, 1-11  Reading for next class sections 1-3 and 1-4 9/15/09 - L1 Crs OvrvwCopyright 2009 - Joanne DeGroat, ECE, OSU24