difference between conditional assignment and if else

What is the difference between:
c = check ? a : b;
and
if(check) c = a;
else c = b;

Highest # of ones or zeros

Design a synchronous sequential circuit to check the highest number of ones and zeros in the last 3 input samples. Your ckt should give 1 at the O/P if the last 3 samples at the input has more 1's similarly 0 when the no. of zeros is high.
Eg:
IN : 001110110000
OUT: 0111111000

Constraints:
1) You are supposed to use only Multiplexers and DFFs for
your design. No external gates. To be specific, 1 4:1 Mux only.
2) Design should be optimized one.
3) Only one clock is available to you. And it is given that the
input is sampled at that clock rate only.

What is the FIFO Depth

It is required to connect a Master, which generates data @ 200 Mega Samples/sec to a Slave which can receive the data @ 10 Mega Samples/Sec. If the data lost in 10Micro Sec, what is the optimal size of FIFO to be used to avoid lose of data?
a. 2000 samples
b. 1900 samples
c. 200 samples
d. 190 samples

# of boolean functions with ‘n’ inputs

How many unique Boolean functions can be there for ‘n’ number of inputs?

Remove short length pulses

It is required to eliminate short length pulses from a sampled data. It means 0’s in continuous 1’s have to be made 1 & similarly 1’s in 0’s are to made 0’s as shown in the following example. Give the FSM for the same.

Eg: I/P 0 1 0 0 1 1 0 1 1 0 0

O/P 0 0 0 0 0 1 1 1 1 1 0