1

PRACTICE MIDTERM

1. Programming

Part a. P= lease change the following while-loop to a for- loop.

int i =3D 1;

int n =3D 1;

while( i > 22 ){

n =3D n + i*i;

i++;

}

Part b. G= iven the following code:

int i =3D 10;

int j =3D 20;

double x =3D 30.0;

provide the values for the following:

<= /o:p>

j/i _______________________

<= /o:p>

j/i*x _______________________

<= /o:p>

x*j/i _______________________

<= /o:p>

x/i _______________________

<= /o:p>

Decide which lines below need to be modified to compil= e. Then make the change(s) necessary. (Use the definitions of i,j and x given above.)

int k =3D = i;

<= /o:p>

int m =3D = x;

<= /o:p>

x =3D = j;

Finite Automata

<= /o:p>

Draw the FA that accepts e= xactly the sentences from this language:

&= nbsp; (AB)*(BA)*

<= /o:p>

2. Turing Machines

<= /o:p>

Look at these rules (#=3Dblank).

<= /o:p>

0 x $ r 1

0 y $ r 0

0 # # r 2

1 x # r 1

1 y $ r 0

1 # # r 2

2 # $ l h

<= /o:p>

Given that the machine starts in state 0 and the head = is on the left most x on this tape

<= /o:p>

xxyyxx##

<= /o:p>

What does the tape look like when the machine halts?

<= /o:p>

<= span style=3D'mso-list:Ignore'>3.&n= bsp; Binary numbers

Given the value 11101010 = in binary (base 2), show the equivalent in decimal (base 10)?

What is the value of 159 = (decimal) in binary?

<= span style=3D'mso-list:Ignore'>4.&n= bsp; Booleans

Fill in the following tru= th table:

a	b	(NOT a) OR (NOT b)<= /p>

&= nbsp; &nbs= p;