GATE CS Digital Logic questions

Let $*$ be defined as $x * y = \bar{x} + y$. Let $z = x * y$. Value of $z * x$ is

What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in Fig

Consider the following state table for a sequential machine. The number of states in the minimized machine will be …

Consider the circuit in figure. $f$ implements

Consider the circuit in below figure which has a four bit binary number $b_3b_2b_1b_0$ as input and a five bit binary number, $d_4d_3d_2d_1d_0$ as output.

Consider the following floating-point number representation. $$\overset{31 \quad \qquad 24 \quad 23 \qquad\quad 0} {\begin{array}{|l|l|}\hline \text{Exponent} & \text{Mantissa} \\ \hline \end{array}}$$ The exponent is in $2’s$ complement representation and the mantissa is in the sign-magnitude representation. The range of the magnitude of the …

Booth’s algorithm for integer multiplication gives worst performance when the multiplier pattern is

A ROM is used to store the table for multiplication of two $8$-bit unsigned integers. The size of ROM required is

A finite state machine with the following state table has a single input $x$ and a single out $z$. …

The number of $1$'s in the binary representation of $(3\ast4096 + 15\ast256 + 5\ast16 + 3)$ are:

What values of $A, B, C$ and $D$ satisfy the following simultaneous Boolean equations? $\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D$

The capacity of a memory unit is defined by the number of words multiplied by the number of bits/word. How many separate address and data lines are needed for a memory of $4K \times 16$?

Find the contents of the flip-flop $Q_2, Q_1$ and $Q_0$ in the circuit of figure, after giving four clock pulses to the clock terminal. Assume $Q_2Q_1Q_0=000$ initially.

State True or False with one line explanation A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits).

The logic expression for the output of the circuit shown in figure below is:

For the initial state of $000$, the function performed by the arrangement of the $\text{J-K}$ flip-flops in figure is:

If the state machine described in figure should have a stable state, the restriction on the inputs is given by

Identify the logic function performed by the circuit shown in figure.

The operation which is commutative but not associative is:

All digital circuits can be realized using only