Boolean Algebra HW #4 Show all intermediate steps (truth tables, algebraic steps, and justifications such as identities or theorems) for full credit. 1. Evaluate the following expression when A = 1, B = O, C = 1, D = 0 F = AB + CD + (A+B)C 2. Find F, the complement of function F, Write your answer using overbars. F(W,X,Y,Z) = WX+YZ+XZ 3. Determine the truth table for the function F=XY+XZ 4. Show with a truth table that the following is true: X(Y+Z) = XY+XZ 5. Simplify the following Boolean expression. Show each simplification step and identity used. a) AB + AB + ABC b) (M+N)(M + P) + MP 6. Find the dual of the Boolean expressions. (swap + with and O with 1; do not complement variables). a) ABC b) (X + Y)(X + Z) c) P+Q+ RS 7. Convert Standard POS form to Canonical POS form. • (A+B)(Ā + C) (B+C) 8. Given that F(a, b, c, d) = Em(1, 3, 4, 6, 8, 9, 12) (i) Write the product of maxterms (canonical POS) for F. (ii) Write the canonical SOP and canonical POS for F.

Consider the following statement, which is intended to assign the value of the expression, the variable result Assume that the double variables. x-ya and b have been properly declared and initialized. (xy) to double result = missing code /: 17 Mark for Review Which of the following can replace / missing code / so that the statement works as intended? Math.sqrt((x + y) 2/ Math.abs(a, b)) Math.sqrt((x + y) 2/ Math.abs(a - b)) Math.sqrt(Math.pow(x + y, 2) / Math. abs(a, b)) Math.sqrt(Math.pow(x + y, 2) / Math.abs (a - b))

Consider the following code segment, which is intended to print the digits of the two-digit int number num in reverse order. For example, if num has the value 75, the code segment should print 57. Assume that num has been properly declared and initialized. /missing code */ System.out.print (onesDigit); System.out.print (tensDigit); 14 Mark for Review Which of the following can be used to replace / missing code so that the code segment works as intended? int onesDigit num 10; int tensDigit num / 10; int onesDigit- num / 10; int tensDigit num 10; int onesDigit -10/num; int tensDigit 10 num; -Undo int onesDigit num 100; Undo int tensDigit-num / 100;

The following code segment is intended to round yal to the nearest integer and print the result double val--0.7 int roundedVal (int) (val +0.51 System.out.println(roundedValu 25 Mark for Review Which of the following best describes the behavior of the code segment? The code segment does not work as intended because the expression (val +0.5) should be cast to a double instead of an int The code segment does not work as intended because val should be cast to an int before 0.5 is added to it. Highlights & Notes Reference Undo Undo The code segment does not work as intended because the expression -Unda positive ר .

In the following code segment, mon and tue are properly declared String variables. String strl-mon.substring(9. mon.indexOf(" "). String str2-tue.substring(tue.indexOf(" ") + 1). System.out.println(strl+and+str2): க 21 Mark for Review For which of the following values of mon and tue will the code segment print "cloudy and foggy"? mon tue "cloudy today" "foggy tomorrow" mon tue "cloudy today" "tomorrow foggy" mon tue "today cloudy" "foggy tomorrow" mon tue "today cloudy" "tomorrow foggy"

G Consider the following code segment, which is intended to assign to num a random integer value between min and max, inclusive, each with an equal chance of being assigned to num. Assume that min and max are integer variables and that the value of max is greater than the value of min. 24 Mark for Review Which of the following can replace /* missing code */ so that the code segment works as intended? double rn = Math.random();_ int num = /* missing code */ ;_ D (int) (rn * max) + min ABC (A) (int) (rn * (max- min)) + min (B (int) (rn * (max min)) + 1 (int) (rn * (max min + 1)) + min

Write the truth table for each of the following logic functions: (a) FX Y+X'. Y'. Z (b) FW' X + Y' · Z' + X' · Z (c) F=W+X' · (Y' + Z) . . (d) F A B+ B' C+C' D + D' A .

Use the theorems of switching algebra to simplify each of the following logic functions: (a) F W X Y Z (W X Y . Z'+W X Y Z (b) FA B+ A . B C D+A B.D. E' + A B C W X Y Z+W X Y' - Z) E + C D E .

Write the canonical sum and product for each of the following logic functions: (a) F = Σx,y(1,2) (c) F=ΣA,B,C(2,4,6,7) = (b) FПAB(0,1,2) (d) F=Пw.x,y(0,1,3,4,5)