CS3410 Homework 1 Review: Karnaugh Maps, FSM, and Performance Analysis Techniques

CS3410 HW1 Review 2014, 2, 21

Agenda • We will go through the HW1 questions together • TAs will then walk around to help

Question 1: Karnaugh Map • Sum of products: • Karnaugh map minimization: • Cover all 1’s • Group adjacent blocks of 2n 1’s that yield a regular shape • Encode common features ab c 00 01 11 10 0 0 0 0 1 1 1 1 0 1

Rules for Karnaugh Map Minimization • Minterms can overlap • Minterms can span 1, 2, 4, 8 … cells • The map can wrap around ab ab c c 00 01 11 10 10 00 01 11 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0

Question 2: Numbers & Arithmetic • Binary translation: • Base conversion via repetitive division • From binary to Hex and Oct • Negating a number (2’s complement) • Overflow • Overflow happened iff carry into msb != carry out of msb

Question 4: FSM

Question 4: FSM (cont.) Spam filter x 2 0 1 2 0 1 0 1 ….. x2 x0 x1 Output Okay

Question 4: FSM (cont.) Spam filter x 2 0 1 2 0 1 0 1 ….. x2 x0 x1 Output Okay SPAM

Question 4: FSM (cont.) State (x1=0, x2=0) and (x1=0, x2=1) have exactly the same transitions AND output. So they are NOT distinct states.

Question 7: Performance • Instruction mix for some program P, assume: • 25% load/store ( 3 cycles / instruction) • 60% arithmetic ( 2 cycles / instruction) • 15% branches ( 1 cycle / instruction) • CPI: • 3 * .25 + 2 * .60 + 1 * .15 = 2.1 • CPU Time = # Instructions x CPI x Clock Cycle Time • Assuming 400k instructions, 30 MHz : • 400k * 2.1 / 30 = 28000 µs (1 µs = 1 microsecond = 1/1M S)

Question 8 Registers and Control are in parallel

Question 8 (cont.) • Refer to section 1.6 in the text book • 4.3.1: The clock cycle time is determined by the critical path (the load instruction) • 4.3.2: • Speedup = • Execution time = cycle time * num of instructions • Speedup < 1 means we are actually slowing down Execution time (old) Execution time (new)

Question 8 (cont.) • 4.3.3: • Cost-performance ratio (CPR) = • The higher, the better • This question asks for a “comparison” of CPR CPR ratio= = * Performance Cost CPR (old) Cost (new) Perf (old) CPR (new) Cost (old) Perf (new) 1 speedup

Question 9/10/11: Assembler Code • Writing the instructions in a human-readable format • http://www.cs.cornell.edu/courses/CS3410/2014sp/MIPS_Vol2.pdf • Core instruction set • http://www.cs.cornell.edu/courses/CS3410/2014sp/project/pa1/pa1.html

Assembler Code • When writing the assembler code: • Decide which register stores which variable • Typically you should use $t0~$t9 and $s0~$s7 (You don’t need to understand their difference now) • Decide which instruction you want to use • Get familiar with the core instruction set • Get familiar with some basic patterns

Basic Assembler Coding Patterns • Arithmetic • C code: • Assembler: a = b + c; #a: $s0, b: $s1, c:$s2 ADD $s0, $s1, $s2

Basic Assembler Coding Patterns • Brunch • C code: • Assembler: if(a < b) //DO A... else //DO B... #a: $s0, b: $s1 SLT $t0, $s0, $s1 BEQ $t0, $zero, POINTB #DO A... POINTB: #DO B...

Basic Assembler Coding Patterns • While loop • C code: • Assembler: while(a < b) //Do something... #a: $s0, b: $s1 LOOP: SLT $t0, $s0, $s1 BEQ $t0, $zero, EXIT #Do something... J LOOP EXIT: #Out of the loop...

Basic Assembler Coding Patterns • Array access • C code: • Assembler: intmyArray[10]; a = myArray[2]; #a: $s0, myArray: $s1 LW $s0, 8($s1)

C Programming • Have you tried the hello-world? • Use csuglab machines. It is easier. • How to read input from the terminal? • scanf: • You need a buffer for it int scanf ( const char * format, ... );

Good Luck! Questions?

CS3410 Homework 1 Review: Karnaugh Maps, FSM, and Performance Analysis Techniques