1
Numerical

### GATE CSE 2016 Set 2

Consider the following database table named $water$_$schemes :$

water_schemes
scheme_no district_name capacity
1 Ajmer 20
1 Bikaner 10
2 Bikaner 10
3 Bikaner 20
1 Churu 10
2 Churu 20
1 Dungargarh 10

The number of tuples returned by the following $SQL$ query is _______________.

with total(name, capacity) as
select district_name, sum(capacity)
from water_schemes
group by district_name
with total_avg(capacity) as
select avg(capacity)
from total
select name
from total, total_avg
where total.capacity ≥ total_avg.capacity

2
Numerical

### GATE CSE 2016 Set 2

Consider an eight-bit ripple-carry adder for computing the sum of $A$ and $B,$ where $A$ and $B$ are integers represented in $2’s$ complement form. If the decimal value of $A$ is one, the decimal value of $B$ that leads to the longest latency for the sum to stabilize is __________ .

3

### GATE CSE 2016 Set 2

Let, ${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$ where ${x_1},\,{x_2},\,{x_3},\,{x_4}$ are Boolean Variables, and $\oplus$ is the $XOR$ operator.

Which one of the following must always be TRUE?

A
${x_1}{x_2}{x_3}{x_4} = 0$
B
${x_1}{x_3} + {x_2} = 0$
C
${\overline x _1} \oplus {\overline x _3} = {\overline x _2} \oplus {\overline x _4}$
D
${x_1} + {x_2} + {x_3} + {x_4} = 0$
4
Numerical

### GATE CSE 2016 Set 2

Let $X$ be the number of distinct $16$-bit integers in $2’s$ complement representation. Let $Y$ be the number of distinct $16$-bit integers in sign magnitude representation.
Then $X −Y$ is ____________.

### Paper Analysis of GATE CSE 2016 Set 2

Subject NameTotal Questions
Algorithms5
Compiler Design3
Computer Networks6
Computer Organization6
Data Structures5
Database Management System4
Digital Logic3
Discrete Mathematics11
Operating Systems3
Theory of Computation6
General Aptitude10