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Essay about ICS 241 Exam 2

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ICS-241
M. Bauer
Exam Two
1. Create a binary search tree from the following data which is as balanced as possible.
No leaf node should be more than +/-1 level from any other leaf node. Note: Do not just create a tree from the data encountered in the following order. 78.2, -35.1, 48.2, 12.9,
-14.7, -86.1, 17.4, 92.7, 38.4, -2.8

17.4

-35.1

-86.1

48.2

-14.7

12.9

38.4

-2.8

78.2

92.7

A
B

C

D
G

E
H

I
L

M

J
N

2. Perform a postorder traversal of the tree depicted above.
•
•
•

Traverse its left subtree.
Traverse is right subtree.
Visit the root of the tree.

•

G, L, H, D, B, M, N, I, E, O, J, P, K, F, C, A

3. Evaluate the following prefix notation expression:
* - * 3 …show more content…

Draw a digital logic circuit for the expression:

8. Find a minimal expansion of

1

1
• xz

1

1

1

+ y z + xz

9. Let G = (V,T,S,P) be the phrase structure grammar with V={0,1,A,B,S}, T={0,1}, and the set of productions P consisting of: S → 0AB, S→ 1B, A → 1B01, B → 100.
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a. Either show that 0110001001 belongs to the language generated by G or explain why it does not.
It is “not” possible to show that 0110001001 because we are looking for a string that
“starts” with a “0” and ends with a “1”. Since we can only use production S with starting state S → 0AB, the string created that will not end with a “1” but always will end with a
“0”.
S → 0AB → 01B01B → 0110001100
b. Either show that 1100 belongs to the language generated by G or explain why it does not. We can show that 1100 belongs to language generated by G by using production S with start state S→ 1B to be:
S→ 1B → 1100

10. Draw a finite state machine (with output) represented by the following state table.
State
s0 s1 s2 s3 s4

f(0) s1 s2 s2 s0 s3 f(1) s3 s4 s1 s4 s0 g(0)
0
1
1
0
1

g(1)
1
0
1
0
0

0,0

S0

0,1

S1 1,0

1,1

1,1

S2

0,1

1,0

0,0

S3

1,0

S4

0,1

11. What is

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