Final Exam Solution CS 213 Fall 2002 ********* Problem 1 ********* Expression Always True? 1. x < 0 => (x*3) < 0 N: x = TMin 2. x < 0 => (dx*dx*dx < 0.0) Y 3. ((y-x)<<3) + x-(2*y) == 6*y - 7*x Y: Associative, commutative, distributes 4. ((x-y)<<3) + (x>>1) - y == N: x = -1, y = 0 8*x - 9*y + x/2 5. (x-y) > 0 => -x < -y N: x = -1, y = TMin 6. ux - x == 0 Y: ux - x = ux + ~x + 1 = 11..1 + 1 = 0 7. x > 0 => !( x >> 31 | !x) == 1 Y: checks for a positive number 8. ((ux >> 1) << 1) = ux N: x = 1 (any number with lsb set) 9. dx / 3.0 == x / 3 N: x/3 == 0 10. x - (int)dx == 0 Y ********* Problem 2 ********* x = 0x44556677 c = 0xcc x = 0xffffffcc c = 0x77 ********* Problem 3 ********* N=10 ********* Problem 4 ********* A. func2 B. func5 ********* Problem 5 ********* int foo(int x, int y) { if (x==0) return y+1; if (y==0) return x+1; return foo(x-1,y) * foo(x, y-1); } ********* Problem 6 ********* The cache holds 128 words. Evict? i j Next conflicting block contents 16 y 8 0 a[8][0..3] 12 n - - a[10][8..11] 14 y 9 2 a[9][2..6] 10 n - - None. Entire array fits in cache ********* Problem 7 ********* Part 1: A. N B. N C. Y D. N E. N Part 2: Parent: i = 10 Child: i = 20 ********* Problem 8 ********* IL ILBT E1LBT E2LBT malloc(n) m+n m+n n n free(bp) 1 1 n 1 isRightFree(bp) 1 1 1 1 isLeftFree(bp) m+n 1 1 1 isValidAddress(p) m+n m+n n n ********* Problem 9 ********* 1. fd3 = 3 2. c = a 3. c = r 4. c = b ********** Problem 10 ********** A. No B. Yes C. No D. No E. Yes