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)?

Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011?$$

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”