Consider the following functional dependencies in a database.
$$\eqalign{ & \,\,\,\,Date\,\,of\,\,Birth\,\, \to \,\,Age \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Age\,\, \to \,\,Eligibility \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Name\,\, \to \,\,Roll\_number \cr & \,\,\,\,\,Roll\_number\,\, \to \,\,Name \cr & Course\_number\, \to \,\,Course\_name \cr & Course\_number\, \to Instructor \cr & (Roll\_Number,\,Course\_number)\,\, \to \,\,Grade \cr} $$

The relation (Roll_number, Name, Date_of_Birth, Age) is

Consider the $$ALU$$ shown below

If the operands are in $$2's$$ complement representation, which of the following operations can be performed by suitably setting the control lines $$K$$ and $${C_0}$$ only ( + and - denote addition and subtraction respectively)?

The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $$(xy + xz)$$ is $$4.$$ What are the minimum possible literal counts of the product -of -sum and sum -of-product representations respectively of the function given by the following Karnaugh map? Here, $$X$$ denotes “don’t care”

Consider the following circuit composed of $$XOR$$ gates are non-inverting buffers.

The non-inverting buffers have delays $${\delta _1} = 2$$ $$ns$$ and $${\delta _2} = 4$$ $$ns$$ as shown in the figure. Both $$XOR$$ gates and all wires have zero delay. Assume that all gate inputs, outputs and wires are stable at logic level $$0$$ at time$$0.$$ If the following waveform is applied at input $$A$$, how many transition(s) (change of logic levels) occurs(s) at $$B$$ during the interval from $$0$$ to $$10$$ $$ns?$$