1. ECEN 248: INTRODUCTION TO DIGITAL DESIGN
Lecture Set A
Dr. S.G.Choi
Dept. of Electrical and Computer Engineering

2. Instructor: Office 333G WERC Office Hours MWF 10-11 AM
Lab Page:

3. Required textbook:
Required Textbook: "Fundamentals of Digital Logic Design" by Brown and Vranesic. VERILOG VERSION
Supplemental texts: "Digital Design: Principles and Practices" by John Wakerly. "Contemporary Logic Design" by Randy Katz.

4. Course info Mailing list: Course website
s will be sent periodically to neo accounts
Announcements:
Lecture cancellations
Deadline extension
Updates, etc.
Course website
All slides, labs, assignments, etc.

5. Grading Policy: Assignments and Labs 25% 3 Hour Exams No Final Exam
20% for 1st exam
25% for 2nd
30% for 3rd
No Final Exam
Quizzes:
Each quiz 1% of the final
Taken into account only if it improves the final grade
Can improve the grade, but no extra points
Final grading may or may not be curved up

6. Quizzes: 3-6 quizzes Multiple choice questions 10-15 minutes
Each quiz 1% of the final
No quiz makeups

7. Grading scale
A standard grading scale will be utilized. The tentative grading scale for the course is: 
A       %
B         80-89%
C        70-79%
D         60-69%
F        Below 59%

8. Course Goals Study methods for
Representation, manipulation, and optimization for both combinatorial and sequential logic
Solving digital design problems
Study HDL description language (verilog)

9. Topics Number bases Logic gates and Boolean Algebra
Gate –label minimization
Combinational Logic
Sequential logic (Latches, Flip-flops, Registers, and Counters)
Memory and Programmable Logic
HDL language (Verilog)

10. Attention over time! t

11. Attention over time! ~5
min t

12. Peer Instruction
Increase real-time learning in lecture, test understanding of concepts vs. details
Complete a “segment” with multiple choice questions
1-2 minutes to decide yourself
3 minutes in pairs/triples to reach consensus. Teach others!
5-7 minute discussion of answers, questions, clarifications

13. The Evolution of Computer Hardware
When was the first transistor invented?
Modern-day electronics began with the invention in 1947 of the transfer resistor - the bi-polar transistor - by Bardeen et.al at Bell Laboratories
For lecture

14. The Evolution of Computer Hardware
When was the first IC (integrated circuit) invented?
In 1958 the IC was born when Jack Kilby at Texas Instruments successfully interconnected, by hand, several transistors, resistors and capacitors on a single substrate
For lecture

15. The Underlying Technologies
Year
Technology
Relative Perf./Unit Cost
1951
Vacuum Tube 1
1965
Transistor 35
1975
Integrated Circuit (IC)
900
1995
Very Large Scale IC (VLSI)
2,400,000
2005
Ultra VLSI
6,200,000,000

16. The PowerPC 750 Introduced in 1999 3.65M transistors
366 MHz clock rate
40 mm2 die size
250nm technology

17. Layers of abstraction ECEN 248 Software Hardware
Application (ex: browser)
Operating
Compiler
System
(Mac OSX)
Software
Assembler
Instruction Set
Architecture
Hardware
Processor
Memory
I/O system
Datapath & Control
ECEN 248
Digital Design
Circuit Design
transistors

18. Technology Trends: Microprocessor Complexity
Itanium 2: 41 Million
Athlon (K7): 22 Million
Alpha 21264: 15 million
Pentium Pro: 5.5 million
PowerPC 620: 6.9 million
Alpha 21164: 9.3 million
Sparc Ultra: 5.2 million
Moore’s Law
2X transistors/Chip
Every 1.5 years
Called
“Moore’s Law”

19. DIGITAL SYSTEMS 19

20. Overview Logic functions with 1’s and 0’s. Truth tables.
Building digital circuitry.
Truth tables.
Logic symbols and waveforms.
Boolean algebra.
Properties of Boolean Algebra
Reducing functions.
Transforming functions.
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21. Digital Systems · Analysis problem:
Determine binary outputs for each combination of inputs
Design problem: given a task, develop a circuit that accomplishes the task
Many possible implementations.
Try to develop “best” circuit based on some criterion (size, power, performance, etc.)
Logic
Circuit
Inputs
Outputs

22. Toll Booth Controller Consider the design of a toll booth controller.
Inputs: quarter, car sensor.
Outputs: gate lift signal, gate close signal
If driver pitches in quarter, raise gate.
When car has cleared gate, close gate.
Logic
Circuit
$·25
Car?
Raise gate
Close gate

23. Describing Circuit Functionality: Inverter
Truth Table A Y 1 A Y
Symbol
Input
Output
Basic logic functions have symbols.
The same functionality can be represented with truth tables·
Truth table completely specifies outputs for all input combinations.
The above circuit is an inverter.
An input of 0 is inverted to a 1.
An input of 1 is inverted to a 0.
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24. The AND Gate A Y B This is an AND gate. So, if the two inputs signals
are asserted (high) the
output will also be asserted.
Otherwise, the output will
be deasserted (low).
Truth Table A B Y 1

25. The OR Gate A Y B This is an OR gate. So, if either of the two
input signals are
asserted, or both of
them are, the output
will be asserted. A B Y 1

26. Describing Circuit Functionality: Waveforms
AND Gate A B Y 1
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Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs·
Waveforms provide another approach for representing functionality.
Values are either high (logic 1) or low (logic 0).
Can you create a truth table from the waveforms?

27. Consider three-input gates
3 Input OR Gate

28. Ordering Boolean Functions
How to interpret A · B+C?
Is it A · B ORed with C ?
Is it A ANDed with B+C ?
Order of precedence for Boolean algebra: AND before OR.
Note that parentheses are needed here :

29. Boolean Algebra
A Boolean algebra is defined as a closed algebraic system containing a set K or two or more elements and the two operators, · and +·
Useful for identifying and minimizing circuit functionality
Identity elements
a + 0 = a
a · 1 = a
0 is the identity element for the + operation·
1 is the identity element for the · operation·

30. Commutativity and Associativity of the Operators
The Commutative Property:
For every a and b in K,
a + b = b + a
a · b = b · a
The Associative Property:
For every a, b, and c in K,
a + (b + c) = (a + b) + c
a · (b · c) = (a · b) · c

31. The Distributive Property
For every a, b, and c in K,
a + ( b · c ) = ( a + b ) · ( a + c )
a · ( b + c ) = ( a · b ) + ( a · c )

32. Distributivity of the Operators and Complements
The Existence of the Complement:
For every a in K there exists a unique element called a’ (complement of a) such that,
a + a’ = 1
a · a’ = 0
To simplify notation, the · operator is frequently omitted. When two elements are written next to each other, the AND (·) operator is implied…
a + b · c = ( a + b ) · ( a + c )
a + bc = ( a + b )( a + c )

33. Duality
The principle of duality is an important concept. This says that if an expression is valid in Boolean algebra, the dual of that expression is also valid.
To form the dual of an expression, replace all + operators with · operators, all · operators with + operators, all ones with zeros, and all zeros with ones.

34. Duality
The principle of duality is an important concept· This says that if an expression is valid in Boolean algebra, the dual of that expression is also valid·
To form the dual of an expression, replace all + operators with · operators, all · operators with + operators, all ones with zeros, and all zeros with ones·
Form the dual of the expression
a + (bc) = (a + b)(a + c)
Following the replacement rules…
a(b + c) = ab + ac
Take care not to alter the location of the parentheses if they are present·

35. Duality
The principle of duality is an important concept· This says that if an expression is valid in Boolean algebra, the dual of that expression is also valid·
To form the dual of an expression, replace all + operators with · operators, all · operators with + operators, all ones with zeros, and all zeros with ones·
Form the dual of the expression
a + (bc) = (a + b)(a + c)
Following the replacement rules…
a(b + c) = ab + ac
Take care not to alter the location of the parentheses if they are present·

36. Involution This theorem states: a’’ = a
Remember that aa’ = 0 and a+a’=1.
Therefore, a’ is the complement of a and a is also the complement of a’.
As the complement of a’ is unique, it follows that a’’=a·
Taking the double inverse of a value will give the initial value.

37. Absorption This theorem states: a + ab = a a(a+b) = a
To prove the first half of this theorem:
a + ab = a · 1 + ab
= a (1 + b)
= a (b + 1)
= a (1)
a + ab = a

38. DeMorgan’s Theorem
A key theorem in simplifying Boolean algebra expression is DeMorgan’s Theorem. It states:
(a + b)’ = a’b’ (ab)’ = a’ + b’
Complement the expression
a(b + z(x + a’)) and simplify.
(a(b+z(x + a’)))’ = a’ + (b + z(x + a’))’
= a’ + b’(z(x + a’))’
= a’ + b’(z’ + (x + a’)’)
= a’ + b’(z’ + x’a’’)
= a’ + b’(z’ + x’a)

39. Postulates and Basic Theorems

40. Summary
Basic logic functions can be made from AND, OR, and NOT (invert) functions.
The behavior of digital circuits can be represented with waveforms, truth tables, or symbols.
Primitive gates can be combined to form larger circuits
Boolean algebra defines how binary variables can be combined.
Rules for associativity, commutativity, and distribution are similar to algebra.
DeMorgan’s rules are important.
Will allow us to reduce circuit sizes.
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Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs·

41. NUMBER SYSTEMS

42. Overview Understanding decimal numbers Binary and octal numbers
The basis of computers!
Conversion between different number systems
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Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

43. Digital Computer Systems
Digital systems consider discrete amounts of data.
Examples
26 letters in the alphabet
10 decimal digits
Larger quantities can be built from discrete values:
Words made of letters
Numbers made of decimal digits (e.g )
Computers operate on binary values (0 and 1)
Easy to represent binary values electrically
Voltages and currents.
Can be implemented using circuits
Create the building blocks of modern computers
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This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

44. Understanding Decimal Numbers
Decimal numbers are made of decimal digits: (0,1,2,3,4,5,6,7,8,9)
Number representation:
8653 = 8x x x x100
What about fractions?
= 9x x x x x x x10-2
Informal notation -> ( )10
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This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

45. Understanding Octal Numbers
Octal numbers are made of octal digits: (0,1,2,3,4,5,6,7)
Number representation:
(4536)8 = 4x83 + 5x82 + 3x81 + 6x80 = (1362)10
What about fractions?
(465.27)8 = 4x82 + 6x81 + 5x80 + 2x x8-2
Octal numbers don’t use digits 8 or 9
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This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

46. Understanding Binary Numbers
Binary numbers are made of binary digits (bits):
0 and 1
Number representation:
(1011)2 = 1x23 + 0x22 + 1x21 + 1x20 = (11)10
What about fractions?
(110.10)2 = 1x22 + 1x21 + 0x20 + 1x x2-2
Groups of eight bits are called a byte
( ) 2
Groups of four bits are called a nibble.
(1101) 2
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We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

47. Why Use Binary Numbers?
Easy to represent 0 and 1 using electrical values.
Possible to tolerate noise.
Easy to transmit data
Easy to build binary circuits.
AND Gate 1

48. Conversion Between Number Bases
Octal(base 8)
Decimal(base 10)
Binary(base 2)
Hexadecimal
(base16)

49. Convert an Integer from Decimal to Another Base
For each digit position:
Divide decimal number by the base (e.g. 2)
The remainder is the lowest-order digit
Repeat first two steps until no divisor remains.
Example for (13)10:
Integer
Quotient
Remainder
Coefficient
13/2 = a0 = 1
6/2 = a1 = 0
3/2 = a2 = 1
1/2 = a3 = 1
Answer (13)10 = (a3 a2 a1 a0)2 = (1101)2

50. Convert an Fraction from Decimal to Another Base
For each digit position:
Multiply decimal number by the base (e.g. 2)
The integer is the highest-order digit
Repeat first two steps until fraction becomes zero.
Example for (0.625)10:
Integer
Fraction
Coefficient
0.625 x 2 = a-1 = 1
0.250 x 2 = a-2 = 0
0.500 x 2 = a-3 = 1
Answer (0.625)10 = (0.a-1 a-2 a-3 )2 = (0.101)2

51. The Growth of Binary Numbers
20=1 1
21=2 2
22=4 3
23=8 4
24=16 5
25=32 6
26=64 7
27=128 n 2n 8
28=256 9
29=512 10
210=1024 11
211=2048 12
212=4096 20
220=1M 30
230=1G 40
240=1T
Kilo
Mega
Giga
Tera

52. Binary Addition 1 1 1 1 1 1 carries 1 1 1 1 0 1 + 1 0 1 1 1
Binary addition is very simple.
This is best shown in an example of adding two binary numbers… 1 1 1 1 1 1
carries
Design state of art organization in 1990 1 1 1

53. Binary Subtraction 1 10 borrows 0 10 10 0 0 10 1 0 0 1 1 0 1
We can also perform subtraction (with borrows in place of carries).
Let’s subtract (10111)2 from ( )2…
borrows
Design state of art organization in 1990

54. Binary Multiplication
Binary multiplication is much the same as decimal multiplication, except that the multiplication operations are much simpler… X
Design state of art organization in 1990

55. Convert an Integer from Decimal to Octal
For each digit position:
Divide decimal number by the base (8)
The remainder is the lowest-order digit
Repeat first two steps until no divisor remains.
Example for (175)10:
Integer
Quotient
Remainder
Coefficient
175/8 = a0 = 7
21/8 = a1 = 5
2/8 = a2 = 2
Answer (175)10 = (a2 a1 a0)2 = (257)8

56. Convert an Fraction from Decimal to Octal
For each digit position:
Multiply decimal number by the base (e.g. 8)
The integer is the highest-order digit
Repeat first two steps until fraction becomes zero.
Example for (0.3125)10:
Integer
Fraction
Coefficient
x 8 = a-1 = 2
x 8 = a-2 = 4
Answer (0.3125)10 = (0.24)8

57. Summary Binary numbers are made of binary digits (bits)
Binary and octal number systems
Conversion between number systems
Addition, subtraction, and multiplication in binary
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This can be an hidden slide. I just want to use this to do my own planning.
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We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

58. HEXADECIMAL NUMBERS

59. Overview Hexadecimal numbers
Related to binary and octal numbers
Conversion between hexadecimal, octal and binary
Value ranges of numbers
Representing positive and negative numbers
Creating the complement of a number
Make a positive number negative (and vice versa)
Why binary?
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This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

60. Understanding Hexadecimal Numbers
Hexadecimal numbers are made of 16 digits:
(0,1,2,3,4,5,6,7,8,9,A, B, C, D, E, F)
Number representation:
(3A9F)16 = 3x x x x160 =
What about fractions?
(2D3.5)16 = 2x x x x16-1 =
Note that each hexadecimal digit can be represented with four bits.
(1110) 2 = (E)16
Groups of four bits are called a nibble.
(1110) 2
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This can be an hidden slide. I just want to use this to do my own planning.
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We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

61. Putting It All Together
Binary, octal, and hexadecimal similar
Easy to build circuits to operate on these representations
Possible to convert between the three formats

62. Converting Between Base 16 and Base 2
3A9F16 = 3 A 9 F
Conversion is easy!
Determine 4-bit value for each hex digit
Note that there are 24 = 16 different values of four bits
Easier to read and write in hexadecimal.
Representations are equivalent!

63. Converting Between Base 16 and Base 8
3A9F16 = 3 A 9 F = 3 5 2 3 7
Convert from Base 16 to Base 2
Regroup bits into groups of three starting from right
Ignore leading zeros
Each group of three bits forms an octal digit.

64. How To Represent Signed Numbers
Plus and minus sign used for decimal numbers: (or +25), -16, etc.
For computers, desirable to represent everything as bits.
Three types of signed binary number representations: signed magnitude, 1’s complement, 2’s complement.
In each case: left-most bit indicates sign: positive (0) or negative (1).
Consider signed magnitude:
= 1210
Sign bit
Magnitude =
Sign bit
Magnitude

65. One’s Complement Representation
The one’s complement of a binary number involves inverting all bits.
1’s comp of is
1’s comp of is
For an n bit number N the 1’s complement is (2n-1) – N.
Called diminished radix complement by Mano since 1’s complement for base (radix 2).
To find negative of 1’s complement number take the 1’s complement.
= 1210
Sign bit
Magnitude =
Sign bit
Magnitude

66. Two’s Complement Representation
The two’s complement of a binary number involves inverting all bits and adding 1.
2’s comp of is
2’s comp of is
For an n bit number N the 2’s complement is (2n-1) – N + 1.
Called radix complement by Mano since 2’s complement for base (radix 2).
To find negative of 2’s complement number take the 2’s complement.
= 1210
Sign bit
Magnitude =
Sign bit
Magnitude

67. Two’s Complement Shortcuts
Algorithm 1 – Simply complement each bit and then add 1 to the result.
Finding the 2’s complement of ( )2 and of its 2’s complement…
N = [N] =
Algorithm 2 – Starting with the least significant bit, copy all of the bits up to and including the first 1 bit and then complementing the remaining bits.
N =
[N] =

68. Finite Number Representation
Machines that use 2’s complement arithmetic can represent integers in the range
-2n-1 <= N <= 2n-1-1
where n is the number of bits available for representing N. Note that 2n-1-1 = ( ) and –2n-1 = ( )2
For 2’s complement more negative numbers than positive.
For 1’s complement two representations for zero.
For an n bit number in base (radix) z there are zn different unsigned values.
(0, 1, …zn-1)

69. 1’s Complement Addition
Using 1’s complement numbers, adding numbers is easy.
For example, suppose we wish to add +(1100)2 and +(0001)2.
Let’s compute (12)10 + (1)10.
(12)10 = +(1100)2 = in 1’s comp.
(1)10 = +(0001)2 = in 1’s comp.
Add carry
Final
Result
Add
Step 1: Add binary numbers
Step 2: Add carry to low-order bit

70. 1’s Complement Subtraction
Using 1’s complement numbers, subtracting numbers is also easy.
For example, suppose we wish to subtract +(0001)2 from +(1100)2.
Let’s compute (12)10 - (1)10.
(12)10 = +(1100)2 = in 1’s comp.
(-1)10 = -(0001)2 = in 1’s comp.

71. 1’s Complement Subtraction
Step 1: Take 1’s complement of 2nd operand
Step 2: Add binary numbers
Step 3: Add carry to low order bit 1
1’s comp
Add
Add carry
Final
Result

72. 2’s Complement Addition
Using 2’s complement numbers, adding numbers is easy.
For example, suppose we wish to add +(1100)2 and +(0001)2.
Let’s compute (12)10 + (1)10.
(12)10 = +(1100)2 = in 2’s comp.
(1)10 = +(0001)2 = in 2’s comp.

73. 2’s Complement Addition
Step 1: Add binary numbers
Step 2: Ignore carry bit
Add
Final
Result
Ignore

74. 2’s Complement Subtraction
Using 2’s complement numbers, follow steps for subtraction
For example, suppose we wish to subtract +(0001)2 from +(1100)2.
Let’s compute (12)10 - (1)10.
(12)10 = +(1100)2 = in 2’s comp.
(-1)10 = -(0001)2 = in 2’s comp.

75. 2’s Complement Subtraction
Step 1: Take 2’s complement of 2nd operand
Step 2: Add binary numbers
Step 3: Ignore carry bit
2’s comp
Add
Final
Result
Ignore
Carry

76. 2’s Complement Subtraction: Example #2
Let’s compute (13)10 – (5)10.
(13)10 = +(1101)2 = (01101)2
(-5)10 = -(0101)2 = (11011)2
Adding these two 5-bit codes…
Discarding the carry bit, the sign bit is seen to be zero, indicating a correct result. Indeed,
(01000)2 = +(1000)2 = +(8)10.
carry

77. 2’s Complement Subtraction: Example #3
Let’s compute (5)10 – (12)10.
(-12)10 = -(1100)2 = (10100)2
(5)10 = +(0101)2 = (00101)2
Adding these two 5-bit codes…
Here, there is no carry bit and the sign bit is 1. This indicates a negative result, which is what we expect. (11001)2 = -(7)10.

78. Binary numbers
Binary numbers can also be represented in octal and hexadecimal
Easy to convert between binary, octal, and hexadecimal
Signed numbers represented in signed magnitude, 1’s complement, and 2’s complement
2’s complement most important (only 1 representation for zero).
Important to understand treatment of sign bit for 1’s and 2’s complement.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

79. Binary Coded Decimal
Digit
BCD Code
0000 5
0101 1
0001 6
0110 2
0010 7
0111 3
0011 8
1000 4
0100 9
1001
Binary coded decimal (BCD) represents each decimal digit with four bits
Ex· =
This is NOT the same as
Why do this? Because people think in decimal.
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bring a computer
die photo
wafer :
This can be an hidden slide· I just want to use this to do my own planning·
I have rearranged Culler’s lecture slides slightly and add more slides· This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20·
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs· 3 2 9

80. Putting It All Together
BCD not very efficient.
Used in early computers (40s, 50s).
Used to encode numbers for seven- segment displays.
Easier to read?

81. Gray Code Gray code is not a number system.
Digit
Binary
Gray Code
0000 1
0001 2
0010
0011 3 4
0100
0110 5
0101
0111 6 7 8
1000
1100 9
1001
1101 10
1010
1111 11
1011
1110 12 13 14 15
Gray code is not a number system.
It is an alternate way to represent four bit data
Only one bit changes from one decimal digit to the next
Useful for reducing errors in communication.
Can be scaled to larger numbers.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide· I just want to use this to do my own planning·
I have rearranged Culler’s lecture slides slightly and add more slides· This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20·
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs·

82. ASCII Code American Standard Code for Information Interchange
ASCII is a 7-bit code, frequently used with an 8th bit for error detection (more about that in a bit).
Character
ASCII (bin)
ASCII (hex)
Decimal
Octal A 41 65
101 B 42 66
102 C 43 67
103 … Z a 1 ‘
credential:
bring a computer
die photo
wafer :
This can be an hidden slide· I just want to use this to do my own planning·
I have rearranged Culler’s lecture slides slightly and add more slides· This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20·
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs·

83. ASCII Codes and Data Transmission
A – Z (26 codes), a – z (26 codes)
0-9 (10 codes), others
Complete listing in Mano text
Transmission susceptible to noise.
Typical transmission rates (1500 Kbps, 56.6 Kbps)
How to keep data transmission accurate?

84. Parity Codes Information Bits P
Parity codes are formed by concatenating a parity bit, P to each code word of C.
In an odd-parity code, the parity bit is specified so that the total number of ones is odd.
In an even-parity code, the parity bit is specified so that the total number of ones is even.
Information Bits P 
Added even parity bit 
Added odd parity bit

85. Parity Code Example
Concatenate a parity bit to the ASCII code for the characters 0, X, and = to produce both odd-parity and even-parity codes.
Character
ASCII
Odd-Parity ASCII
Even-Parity ASCII X =

86. Binary Data Storage Binary cells store individual bits of data
Multiple cells form a register.
Data in registers can indicate different values
Hex (decimal)
BCD
ASCII 1 1 1 1
Binary Cell

87. Register Transfer Data can move from register to register.
Digital logic used to process data.
We will learn to design this logic.
Register A
Register B
Register C
Digital Logic
Circuits

88. Transfer of Information
Data input at keyboard
Shifted into place
Stored in memory
NOTE: Data input in ASCII

89. Building a Computer We need processing We need storage
We need communication
You will learn to use and design these components.

90. Summary
Although 2’s complement most important, other number codes exist.
ASCII code used to represent characters (including those on the keyboard).
Registers store binary data.
Next time: Building logic circuits!
credential:
bring a computer
die photo
wafer :
This can be an hidden slide· I just want to use this to do my own planning·
I have rearranged Culler’s lecture slides slightly and add more slides· This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20·
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs·