2. Given that F = X[Y + Z(Q + R)], find F

3. Two completely specified functions are f(A,B,C) = (0, 1, 4, 7) and g(A,B,C) = (0, 3, 4, 6, 7). a) Express the maxterms of f in algebraic form. (8 pts) b) Explain how to find the minterms of f + g (f OR g) and list them in decimal form. (8 pts) c) Explain how to find the minterms of f g (f AND g) and list them in decimal form. (8 pts)

4. An incompletely specified function f(A,B,C,D) is given in the Karnaugh map below. (16 pts) a) Find all possible prime implicants (minimal products) of f. Express the prime implicants in algebraic form. (You do not have to find a minimal solution.) b) Find all possible prime implicates (minimal sums) of f. Express the prime implicates in algebraic form. (You do not have to find a minimal solution.)

6. Using only 2-input NAND gates, implement F = WXY + WZ + YZ. (8 pts)

7. Using an 8-bit 2s complement notation (MSB is the sign bit), convert the following numbers to binary and perform the indicated arithmetic operations in binary. Give the 8-bit result in 2s complement form and indicate if overflow occurs on any of the operations. (10 pts) i) 4710 - 7410 ii) 8610 + 5110 .

8. Fill in the blank cells in the following table by making the indicated conversions. (10 pts) decimal 69.75, Hexadecimal 3E.A