Boolean Algebra
Q11.
Consider the minterm list form of a Boolean function F given below. F(P,Q,R,S)=\sum m(0,2,5,7,9,11)+d(3,8,10,12,14) Here, m denotes a minterm and d denotes a don't care term. The number of essential prime implicants of the function F is ______.Q12.
Consider the Karnaugh map given below, where x represents "don't care" and blank represents 0. Assume for all inputs (a, b, c, d) the respective complements (\bar{a},\bar{b},\bar{c},\bar{d}) are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________.Q13.
Let \bigoplus and \bigodot denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?Q14.
What is the minimum number of two-input NAND gates used to perform the function of two-input OR gate?Q15.
Given f(w,x,y,z) = \sum_{m} (0,1,2,3,7,8,10) + \sum_{d} (5,6,11,15), where d represents the don't care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w,x,y,z) ?Q17.
If w, x, y, z are Boolean variables, then which one of the following is INCORRECT ?Q19.
In the diagram above, the inverter (NOT gate) and the AND-gates labeled 1 and 2 have delays of 9, 10 and 12 nanoseconds (ns), respectively. Wire delays are negligible. For certain values a and c, together with certain transition of b, a glitch (spurious output) is generated for a short time, after which the output assumes its correct value. The duration of glitch is:Q20.
The simplified SOP (Sum of Product) from the Boolean expression(P + \bar{Q} + \bar{R}) . (P + {Q} + R) . (P + Q +\bar{R})is