Boolean Algebra
Q1.
The following circuit compares two 2-bit binary numbers, X and Y represented by X_{1}X_{0} and Y_{1}Y_{0} respectively. (X_{0} and Y_{0} represent Least Significant Bits)Under what conditions Z will be 1?Q2.
Any set of Boolean operation that is sufficient to represent all Boolean expression is said to be complete. Which of the following is not complete ?Q3.
Consider the following Boolean expression. F=(X+Y+Z)(\overline X +Y)(\overline Y +Z) Which of the following Boolean expressions is/are equivalent to \overline F (complement of F)?[MSQ]Q4.
What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = \Sigma (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________ .Q5.
Consider three 4-variable functions f_1,f_2 \; and \; f_3, which are expressed in sum-of-minterms f_1=\Sigma (0,2,5,8,14) f_2=\Sigma (2,3,6,8,14,15) f_3=\Sigma (2,7,11,14) For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:Q6.
Minimum number of NAND gates required to implement the following binary equationY=(\bar{A}+\bar{B})(C+D)Q8.
If ABCD is a 4-bit binary number, then what is the code generated by the following circuit?Q9.
Consider the Boolean function z(a,b,c). Which one of the following minterm lists represents the circuit given above?Q10.
Consider a Boolean function f(w,x,y,z) such that \begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array} The number of literals in the minimal sum-of-products expression of f is ________