Review for Midterm 1

1. Review for Midterm 1 CPSC 321 Computer Architecture Andreas Klappenecker

2. Administrative Issues • Office hours have been moved: • Wednesday October 15 and 22 canceled • Thursday October 16 and 23 @ 2:00pm-3:00pm • Talk by Bjarne Stroustrup • today @ 4:10pm, HRBB 124

3. Reading Assignments • Chapter 1,2,3,4, Appendix B • How does the algorithm work? • What is the complexity of the algorithm? • Work some examples • Get familiar with number representations • Assembly programming, the gory details • Combinatorial circuits • Read keyword list first, then the chapter

4. Early History • 1938 Zuse’s Z1 • electromechanical, experimental • Zuse’s Z2 almost identical to Z1 • 1941 Zuse’s Z3 • first reliable, freely programmable computer • memory based on relays • did not have stored program concept • Turing-complete

5. Early History • 1943-44 Mark 1 Colossus • memory based on vacuum tubes • special purpose machine, not Turing complete • but it had some flexibility • used in Bletchley Park to break the fish cipher

6. Early History • 1944 Harvard Mark I by Aiken and team • decimal number system • memory based on relays • 1945 ENIAC by Eckert and Mauchly • memory based on vacuum tubes • 1945 von Neumann et al. • introduce the stored program principle • incorporated in EDVAC design

7. Questions • How was the memory of xyz realized? • Was xyz Turing-complete? • Who designed xyz? • …

8. MIPS Assembly Language • Complete a template program • What does the code fragment do? • Stack usage for recursive procedures • know every nut, bolt and screw • slightly different skills needed • Know your [pseudo]instructions • Is blt a,b,c an instruction?

9. MIPS Addressing Modes • Immediate addressing • Register addressing • Base displacement addressing • PC-relative addressing • address is the sum of the PC and a constant in the instruction • Pseudo-direct addressing • jump address is 26bits of instruction concatenated with upper bits of PC

11. Addressing Modes • Register Addressing • add $s1, $s2, $s3 • $s1 = $s2 + $s3 • Immediate Addressing • addi $s1, $s2, 100 • $s1 = $s2 + 100

12. Addressing Modes • Base addressing • lw $s1, 100($s2) • $s1 = Memory[$s2+100] • PC-relative branch • beq $s1, $s2, 25 • if ($s1 == $s2) goto PC + 4 + 100

13. Addressing Modes • Pseudo-direct addressing • j 1000 • goto 1000 • concatenate 26bit address with upper bits of the PC • Study section 3.8 for further details • In particular, get used to Figure 3.18

14. Arithmetic • Know how to add and subtract • Know when overflow occurs • Be able to construct an ALU • or something like that • Carry lookahead

15. Idea of Carry Lookahead cout=ab+cin(a xor b) =ab+acin+bcin =ab+(a+b)cin = g + p cin Generate g = ab Propagate p = a+b

16. Carry Lookahead Iterate the idea, generate and propagate ci+1 = gi + pici = gi + pi(gi-1 + pi-1 ci-1) = gi + pigi-1+ pipi-1ci-1 = gi + pigi-1+ pipi-1gi-2 +…+ pipi-1 …p1g0 +pipi-1 …p1p0c0 Two level AND-OR circuit Carry is known early!

17. Booth’s Multiplication • Looking at 2 bits of multiplier • If the bits are • 00 => do nothing • 10 => beginning run of 1’s: subtract • 01 => end of run of 1’s: add • 11 => do nothing

18. Booth’s Multiplication • Multiply 0010 by 0110 = 00001100 0000 00100 sub [= add 11111100] 000000 0010000 add [= add 00010000] 0001100

19. Floating Point • Know the IEEE 754 representation • sign bit s • exponent E with 8 bits • significand S with 23 bits • bias 127 • (-1)s x (1+S)x2(E-127) • Given: 32 bits, interpret • Know all conversions

20. Final Remarks • Use exercises at end of chapter to check knowledge • Answers are usually easy to figure out with the help of the text • Do not cheat! Read the text carefully, then attempt to solve the problems • Appendices A and B are useful bedtime reading • There is a need for speed!