1. Computer Fundamentals ELEC 330 Digital Systems Engineering Dr. Ron Hayne

2. 330_012 Review of Number Systems  Number Systems (Conversions) Binary Octal Hex  Negative Numbers Two’s Complement Sign Extension  Arithmetic Addition (Subtraction)  Codes BCD ASCII

3. 330_013 Positional Number Systems

4. 330_014 Binary

5. 330_015 Number Systems

6. 330_016 Octal and Hexadecimal

7. 330_017 Octal and Hexadecimal

8. 330_018 Conversions 13.375 10 = ? 2 132 6 R 12 3 R 02 1 R 12 0 R 1 (MSB) 0.375 x 2 = 0.75 0.75 x 2 = 1.5 0.5 x 2 = 1.0 (LSB) 13.375 10 = 1101.011 2

9. 330_019 Binary Addition (Full Adder) C IN XYC OUT S 00000 00101 01001 01110 10001 10110 11010 11111

10. 330_0110 4-bit Addition Example X + Y S 0 + 100 1100 0 1 0 0 1 1 0 0 0 2 + 3 5

11. 330_0111 Negative Numbers

12. 330_0112 Two’s Complement  MSB serves as sign bit (fixed-width) 0 => positive 1 => negative  Negation Operation Complement all bits Add 1  Alternate Negation Operation Starting from right to left Copy up to and including the first 1 Complement the rest

13. 330_0113 2 = -6 10 2 = +6 10 Two’s Complement (4-bit) +6 10 = 0110 2 1001 +1 1010 2 = -6 10 10 0101 +1 0110 2 = +6 10 1001

14. 330_0114 Two’s Complement Arithmetic  Examples (4-bit) 3 - 6 = -3 -4 - 5 = ?

15. 330_0115 Overflow  Operation produces a result that exceeds the number system  Example (4-bits) Range -8 to +7  Detection Rule Overflow occurs if the addends’ signs are the same, but the sum’s sign is different from the addends’

16. 330_0116 Sign Extension  Converting a Two’s Complement Number to an Equivalent with More Bits 4-bit to 8-bit 8-bit to 16-bit  Reproduce the Sign Bit +6 = 0110 4-bit = 00000110 8-bit -6 = 1010 4-bit = 11111010 8-bit

17. 330_0117 Binary-Coded Decimal (BCD)  Encodes digits 0 thru 9  4-bit unsigned binary 0000 thru 1001  6 unused code words 1010 thru 1111  Packed BCD 8-bit byte 2 BCD digits

18. 330_0118 BCD Arithmetic  Correction made if result exceeds 1001 Add 6 Produces carry 36 0011 0110 + 27 + 0010 0111 63 0101 1101 + 0000 0110 0110 0011

19. 330_0119 Character Codes  ASCII (7-bits) American Standard Code for Information Interchange

20. 330_0120 Summary  Number Systems (Conversions) Binary Octal Hex  Negative Numbers Two’s Complement Sign Extension  Arithmetic Addition (Subtraction)  Codes BCD ASCII

21. 330_0121 Digital Systems  Logic Gates  Building Blocks Combinational Sequential Memory  Examples Synchronous Serial Communications Instruction-controlled Information Processor

22. 330_0122 Logic Gates X  Y X  Y X _

23. 330_0123 More Logic Gates X  Y _____ X  Y _____

24. 330_0124 Binary Decoder (n-to-2 n )  Activates exactly one of 2 n outputs based on an n-bit input value

25. 330_0125 Multiplexer  Digital Switch Selects 1 of n sources Based on s control lines n = 2 s Sources b bits wide

26. 330_0126 Arithmetic Logic Unit (ALU)

27. 330_0127 Edge-Triggered D Flip-Flop

28. 330_0128 4-bit Binary Counter  Synchronous Active-low Load Active-low Clear  Two Enables ENP (parallel) ENT  Ripple Carry Out RCO (ENT) Cascading

29. 330_0129 Universal Shift Register

30. 330_0130 Register Notation  Serial Transfer  Parallel Transfer  Register Contents RC Logical Shift Left0 R 1 0 1 1 0 1 0 1B 5

31. 330_0131 Buses and Transfer Gates Transfer 8 8

32. 330_0132 Memory Organization  Dimensions n-bit words k-bit address  Operations Read, Load, Fetch Write, Store Memory first word next word last word n bits Address 0 1 2 k -1......

33. 330_0133 Memory  Memory Signals  Memory Model Mem Address Data Read/Write Clock 0000    C329B6 C23AC1 C23B33    FFFF22

34. 330_0134 Example Digital System  Synchronous Serial Communications Parallel Register Shift Register Control Unit CountF Slave Device Master Device Transmit Receive Clock

35. 330_0135 Example Digital System  Instruction-controlled Information Processor Arithmetic Logic Unit Registers Transfer Gates Input Port Output Port Control Unit

36. ALU AB OUT Processor XIN LALB XAXB LOUT C0 C1 Control Unit C0 C1 XA XB LA LB XIN LOUT Clock OUT IN C0 C1Operation 00 IN1 + IN2  OUT 01 IN1 + IN2 + 1  OUT 10 IN1 + IN2  OUT 11 IN1 + IN2 + 1  OUT

37. 330_0137 System Operation  IN - B  OUT Control Signals StepRTLXINLALBXAXBC0C1LOUT 1 IN  A 11000000 2 A - B  A 01011110 3 A  OUT X00XXXX1

38. 330_0138 Summary  Logic Gates  Building Blocks Combinational Sequential Memory  Examples Synchronous Serial Communications Instruction-controlled Information Processor

39. 330_0139 Processors  Stored Program Processors  General-Purpose Computers  Microprocessors  Microcomputers  Microcontrollers

40. 330_0140 Building Blocks  Clock  Processor ALU Registers  Control Unit  Memory  Input/Output

41. 330_0141 Stored Program Processor Input/ Output Processor Control Unit In Out Data Memory Data Control Instruction Control/Status Clock

42. 330_0142 Memory  Instructions Program Software  Data Load Store  Memory Model 0000    C329B6 C23AC1 C23B33    FFFF22

43. 330_0143 Instruction Operation  Fetch Phase PC Program Counter IR Instruction Register M[PC]  IR PC + 1  PC  Execute Phase Instruction dependent Example: Load Accumulator A LDAA $34 M[34]  A

44. 330_0144 General-Purpose Computer  Arithmetic Operations  Logical Operations  Load and Store Operations  Testing and Branching  Input and Output

45. 330_0145 Computer Architecture  Princeton  von Neumann Memory holds both instructions and data Input/ Output Processor Control Unit In Out Data Memory Data Control Instruction Control/Status Clock

46. 330_0146 Computer Architecture  Harvard Separate instruction and data memories Input/ Output Processor Control Unit In Out Data Memory Data Control Instruction Control/Status Clock Instruction Memory

47. 330_0147 Microprocessor/Microcomputer  Microprocessor Single Integrated Circuit (IC) Processor and Control Unit  Microcomputer Single Printed Circuit Board Interconnection of multiple ICs Microprocessor, Memory, I/O, Clock  Microcontroller Single-Chip Microcomputer

48. 330_0148 Microcomputer/Microcontroller Input/ Output Processor Control Unit Memory Clock Microcomputer/Microcontroller Microprocessor

49. 330_0149 Embedded Control Systems  Microcomputer inside a device that is not called a computer Satellite TV Receivers Microwave Ovens Programmable Thermostats Automobiles Robotics

50. 330_0150 Personal Computers  PC Collection of components that contain many microcomputers Central Microcomputer (CPU) Keyboard Controller Disk Drive Interface Display Monitor Interface Printer

51. 330_0151 Summary  Stored Program Processors  General-Purpose Computers  Microprocessors  Microcomputers  Microcontrollers