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1. Org remarks • Parts of the book which can be read: • 4th edition: • Chapter 1: pages 3-31 • Chapter 2: pages 35-91 • Chapter 3: examples 3.4 and 3.5; pages 115-139 • Chapter 4: pages 149-170 • Chapter 5: pages 207-222 • 3d edition: • Chapter 1 • Chapter 2: pages 29-65; sections 2.7-2.9 • Chapter 4: 141-166 • Chapter 5: 201-233 • Chapter 6: 241-258 Digital Techniques Fall 2007 André Deutz, Leiden University

2. Onto Our Simple One-cycle Instruction Processor • CLUs: Continuation of ALU discussion • CLUs: discussion of algorithms and hardware for multiplication (and discuss the idea of Booth’s algorithm) • Sequential Circuits: Ways of clocking flip-flops • Von Neumann Computer Model • Implementation of the fetch-part of the eternal von Neumann cycle Digital Techniques Fall 2007 André Deutz, Leiden University

3. An old acquaintance: processor-project assignment 1 (1.3) a b c_in k_1 k_0 2 0 1 r(esult) 1-bit ALU as specified in 1.3 2 + 3 c_out Digital Techniques Fall 2007 André Deutz, Leiden University

4. An old acquaintance: processor-project assignment 1 (1.3): 1-bit ALU a b c_in k_1 k_0 2 Let us find another implementation Of the 1-bit ALU by constructing The Truth table for r(esult) and c_out Subsequently read off the canonical Sum of minterms for r and c_out, simplify this sum With the Quine-McCluskey Algorithm. Convert the minimized sums into LDs. 0 1 r(esult) 2 + 3 c_out Digital Techniques Fall 2007 André Deutz, Leiden University

5. 1-bit ALU specified in 1.3TT for r and c_out Digital Techniques Fall 2007 André Deutz, Leiden University

6. Canonical sum for r(esult) and c_out We continue with r: Digital Techniques Fall 2007 André Deutz, Leiden University

7. Simplification of the expression for r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

8. Simplification of the expression for r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

9. Simplification of the expression for r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

10. Simplification of the expression for r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

11. Simplification of the expressionfor r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

12. Simplification of the expressionfor r by Quine-McCluskey The red one are the essential prime implicants Digital Techniques Fall 2007 André Deutz, Leiden University

13. Simplification of the expression for r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

14. Simplification of the expressionfor r by Quine-McCluskey Digital Techniques Fall 2007 André Deutz, Leiden University

15. Construction of LD for r: Digital Techniques Fall 2007 André Deutz, Leiden University

16. A more realistic ALU Digital Techniques Fall 2007 André Deutz, Leiden University

17. A more realistic ALU: the MSB slice Digital Techniques Fall 2007 André Deutz, Leiden University

18. A more realistic ALU carryOut Digital Techniques Fall 2007 André Deutz, Leiden University

19. Answer to the question of Lecture #1: Bits have no inherent meaning: operations determine whether they are really ASCII characters, integers, floating point numbers … The previous slide (the ALU) makes this point quite tangible! The choice of operation will determine whether the bitstrings a_3a_2a_1a_0 , b_3b_2b_1b_0 and the output bitstring result_3result_2result_1result_0 are viewed as two’s complement (numbers -8 through +7, for a 4-bit ALU) or as binary (numbers 0 through +15). Digital Techniques Fall 2007 André Deutz, Leiden University

20. Multiplication: towards Booth’s Algorithm Digital Techniques Fall 2007 André Deutz, Leiden University

21. Multiplication: first attempt 32 bits Shift left 64 bits 64 64 64 bits Digital Techniques Fall 2007 André Deutz, Leiden University

22. Multiplication: second attempt Hardware: Digital Techniques Fall 2007 André Deutz, Leiden University

23. Multiplication: second attempt Digital Techniques Fall 2007 André Deutz, Leiden University

24. Multiplication: third attempt Digital Techniques Fall 2007 André Deutz, Leiden University

25. Multiplication: third attempt Digital Techniques Fall 2007 André Deutz, Leiden University

26. Multiplication: Booth’s algorithm • What about signed multiplication? • easiest solution is to make both positive & remember whether to complement product when done (leave out the sign bit, run for 31 steps) • Booth’s Algorithm is more elegant way to multiply signed numbers using same hardware as before Digital Techniques Fall 2007 André Deutz, Leiden University

27. Motivation for Booth’s algorithm Digital Techniques Fall 2007 André Deutz, Leiden University

28. Booth’s Algorithm Insight Current Bit Bit to the Right Explanation Example 1 0 Beginning of a run of 1s 0001111000 1 1 Middle of a run of 1s 0001111000 0 1 End of a run of 1s 0001111000 0 0 Middle of a run of 0s 0001111000 Originally for Speed since shift faster than add for his machine

29. Booth’s Algorithm 1. Depending on the current and previous bits, do one of the following:00: a. Middle of a string of 0s, so no arithmetic operations.01: b. End of a string of 1s, so add the multiplicand to the left half of the product.10: c. Beginning of a string of 1s, so subtract the multiplicand from the left half of the product.11: d. Middle of a string of 1s, so no arithmetic operation. 2. As in the previous algorithm, shift the Product register right (arith) 1 bit. Multiplicand Product (2 x 3)0010 0000 0011 0 Multiplicand Product (2 x -3)0010 0000 1101 0

30. Digital Techniques Fall 2007 André Deutz, Leiden University

31. Sequential circuits • Ways of triggering flip-flops • Whenever the clock is asserted (level sensitive) • Whenever the clock changes state (edge-sensitive) • Capture data on one edge of the clock and transfer it to the output of the following edge(i.e, master-slave flip-flop) Digital Techniques Fall 2007 André Deutz, Leiden University

32. Digital Techniques Fall 2007 André Deutz, Leiden University

33. The von Neumann Model of a computer Digital Techniques Fall 2007 André Deutz, Leiden University

34. A typical “desktop” system: Digital Techniques Fall 2007 André Deutz, Leiden University

35. Where is the processor? Digital Techniques Fall 2007 André Deutz, Leiden University

36. A look at the motherboard: Digital Techniques Fall 2007 André Deutz, Leiden University

37. Basic functional blocks of a simple computer Digital Techniques Fall 2007 André Deutz, Leiden University Digital Techniques Fall 2007 André Deutz, Leiden University

38. Basic functional blocks of a simple computer • The CPU, or processor, consists of a datapath and control • The datapath performs arithmetic and logical operations on data stored temporarily in internal registers • The control unit determines exactly what operations are performed. It also controls acccess to memory and I/O devices Digital Techniques Fall 2007 André Deutz, Leiden University

39. Salient feature of the von Neumann Architecture Storage/memory structure holds both a list of instructions (= program) and data The list of instructions and the data are changeable, making the computer into a universal machine (as opposed to calculators). Digital Techniques Fall 2007 André Deutz, Leiden University

40. Instruction Processing (von Neumann Cycle -- eternal) Fetch instruction from memory (Increment program counter ) Execute instruction How do you stop this? 4-40 Digital Techniques Fall 2007 André Deutz, Leiden University

41. Instruction Processing in more detail Fetch instruction from memory (Increment program counter) Decode instruction Evaluate address Fetch operands from memory Execute operation Store result 4-41 Digital Techniques Fall 2007 André Deutz, Leiden University

42. Digital Techniques Fall 2007 André Deutz, Leiden University

43. Von Neumann model • Discussion of model • Eternal von Neumann cycle • Show-and-tell: Digital Works implementation of fetch part of the eternal von Neumann cycle Digital Techniques Fall 2007 André Deutz, Leiden University

44. Some Details for building our computer Digital Techniques Fall 2007 André Deutz, Leiden University

45. Single cycle data paths: Assumptions All state elements act like positive edge-triggered flip flops. D Q clk Processor uses synchronous logic design (a “clock”). Reset ? Digital Techniques Fall 2007 André Deutz, Leiden University

46. A portion of the datapath used for Fetching instructions and incrementing The program counter (PC) Instr Mem Addr Data + 0x1 PC D Q

47. How data flows after posedge op RegFile Instr Mem 5 rs1 32 32 5 rd1 rs2 5 Addr Data ws 32 32 ALU + Logic rd2 wd 0x1 WE 32 32 PC D Q Digital Techniques Fall 2007 André Deutz, Leiden University

48. registerfile Chooses first register 4-bit register 4-bit register 4-bit register 4-bit register Data to read from First chosen register Chooses second register Chooses register to be written Data to read from Second chosen register Data to be written Write Enable Digital Techniques Fall 2007 André Deutz, Leiden University Digital Techniques Fall 2007 André Deutz, Leiden University