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”

A 1- input, 2- output synchronous sequential circuit behaves as follows.

Let $${z_k},\,{n_k}$$ denote the number of $$0’s$$ and $$1’s$$ respectively in initial $$k$$ bits of the input

$$\left({{z_k} + {n_k} = k} \right).$$ The circuit outputs $$00$$ until one of the following conditions holds.

$$ * \,\,\,\,\,$$ $${z_k} = {n_k} + 2.\,\,\,$$ In this case, the output at the $$k$$-th and all subsequent clock ticks is $$10.$$

$$ * \,\,\,\,\,$$ $${n_k} = {z_k} + 2.\,\,\,$$ In this case, the output at the $$k$$-th and all subsequent clock ticks is $$01.$$

What is the minimum number of states required in the state transition graph of the above circuit?