1
GATE CSE 2003
+1
-0.3
Assuming all numbers are in $$2's$$ complement representation, which of the following numbers is divisible by $$11111011?$$
A
$$11100111$$
B
$$11100100$$
C
$$11010111$$
D
$$11011011$$
2
GATE CSE 2003
+2
-0.6
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
$$(11, 9)$$
B
$$(9,13)$$
C
$$(9,10)$$
D
$$(11, 11)$$
3
GATE CSE 2003
+5
-1.5
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 $$10$$ $$ns?$$ A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
4
GATE CSE 2003
+2
-0.6
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?

A
$$5$$
B
$$6$$
C
$$7$$
D
$$8$$
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