GATE Computer Science Engineering(CSE) 2027 Test: Boolean Algebra & Logic

The function

can be written as

The Karnaugh map for the Boolean function F of 4 Boolean variables is given in Figure. A, B, C are don't care conditions. What values of A, B, C will result in the minimal expression?

Let f(A, B) =   then simplified from of the function 

Consider the circuit-shown below. Each of the control inputs, C₀ through C₃, must be tied to a constant, either ‘0’ or '1'.

What are the values of C₀ through C₃ that would cause F to be the exclusive OR of A and B?

Write the minimized expression of the function of three variables that is 1 if the third variable is equal to the OR of the first two variable, 0 otherwise

Which of the following functions implements the Karnaugh map shown below?

The Boolean expression for the shaded area in the given Venn diagram is

The Boolean expression is a simplified version of expression:

Then which of the following choice is correct:
1. Don’t care conditions don’t exist.
2. Don’t care conditions exist.
3. D (16, 18, 20, 23, 27, 29) is the set of don’t care conditions.
​4. D (16, 20, 22, 27, 29) is the set of don’t care conditions.

The logical expression for K-Map shown above is:

The Boolean expression for the shaded area in the Venn diagram is

Consider, a four variable Boolean function, which contains half the number of minterms with odd number of 1 ’s. Then the Boolean can be realized with variables A, B, C, D as:

Consider

the Y is equivalent to:

An X-Y flip-flop, whose characteristic table is given below, is to be implemented using a JK flip-flop. This can be done by making

For what logic gate, the output is complement of the input?

The NAND can function as a NOT gate if