Digital Logic & Number representation

Question 261

Choose the correct choice(s) regarding the following proportional logic assertion S:

S:((P∧Q)→R)→((P∧Q)→(Q→R)) 

• S is neither a tautology nor a contradiction
• S is a tautology
• S is a contradiction
• The antecedent of S is logically equivalent to the consequent of S

Question 262

If x and y are two decimal digits and (0.1101)₂ = (0.8xy5)₁₀, the decimal value of x+y is _____ .

• 3
• 4
• 1
• 2

Question 263

Consider a Boolean function f(w,x,y,z) such that

f(w,0,0,z) = 1
f(1,x,1,z) = x+z
f(w,1,y,z) = wz+y

The number of literals in the minimal sum-of-products expression of f is _________ .

• 6
• 3
• 8
• 1

Question 264

Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

• R1 = 1011 and R2 = 1110

• R1 = 1100 and R2 = 1010

• R1 = 0011 and R2 = 0100

• R1 = 1001 and R2 = 1111