GATE CS Digital Logic questions

The amount of ROM needed to implement a $4\text{-bit}$ multiplier is

The decimal value $0.5$ in IEEE single precision floating point representation has

The truth table ${\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\ \hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\ \hline 1& 1& 1 \\ \hline \end{array}}$ represents the Boolean function

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If all the flip-flops were reset to $0$ at power on, what is the total number of distinct outputs (states) represented by $PQR$ generated by the counter?

Consider the following circuit involving three D-type flip-flops used in a certain type of counter configuration. If at some instance prior to the occurrence of the clock edge, $P, Q$ and $R$ have a value $0$, $1$ and $0$ respectively, what shall be the value of $PQR$ after the clock edge?

The minimum number of $\text{D}$ flip-flops needed to design a mod-258 counter is

The simplified SOP (Sum of Product) from the Boolean expression $$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$$ is

In the sequential circuit shown below, if the initial value of the output $Q_1Q_0$ is $00$. What are the next four values of $Q_1Q_0$?

What is the boolean expression for the output $f$ of the combinational logic circuit of NOR gates given below?

The Boolean expression of the output $f$ of the multiplexer shown below is

$P$ is a $16$-bit signed integer. The $2$'s complement representation of $P$ is $(F87B)_{16}$. The $2$'s complement representation of $8\times P$ is

The main memory unit with a capacity of $4$ $\text{megabytes}$ is built using $1\text{M} \times \text{1-bit}$ DRAM chips. Each DRAM chip has $1\text{K}$ rows of cells with $1\text{K}$ cells in each row. The time taken for a single refresh operation is $100\; \text{nanoseconds}$. The time required to perform one refresh operation on all the cells …

The minterm expansion of $f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}$ is

Given the following state table of an FSM with two states $A$ and $B$,one input and one output. …

How many $32K \times 1$ RAM chips are needed to provide a memory capacity of $256K$ bytes?

What is the minimum number of gates required to implement the Boolean function $\text{(AB+C)}$ if we have to use only $2\text{-input NOR}$ gates?

$(1217)_8$ is equivalent to

If $P, Q, R$ are Boolean variables, then $(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})$ simplifies to

Given $f_1$, $f_3$ and $f$ in canonical sum of products form (in decimal) for the circuit $f_1 = \Sigma m(4, 5, 6, 7, 8)$ $f_3 = \Sigma m(1, 6, 15)$ $f = \Sigma m(1, 6, 8, 15)$ then $f_2$ is

Let $r$ denote number system radix. The only value(s) of $r$ that satisfy the equation $\sqrt{121_r}={11}_r$ is/are