Binary Coding

carlospro7

I'm not sure if this is the right place to post this but anyway...

I was given this assignment on binary numbers. The object is to pinpoint the location of this certain doughnut that is in this set of doughtnuts and it's divided in 4 sets of 4. Like this:

OO OO
OO OO

OO OO
QO OO

The Q being the doughnut that i need to pinpoint. Now I have to locate this doughnut using a binary code and can only be a maximum of 5-bits. The question it says is "devise two code schemes for pinpointing the location of the blue (Q) doughnut with the MSB (Most significant bit) giving the order of directions." I'm not entirely sure what that means, and while this may be a stupid question, what exactly is a code scheme? I'm new at this, and it'd be great if someone could help me with it. Thanks in advance.

AftershockVibe

Erm... I have to admit that I'm not entirely sure what the question wants as an answer as it has no context. But here is what I would hazard a guess it means...

You have 5 bits:
XXXXX; where X= 0/1

MSB indicates "direction order" (which comes later) so you have:
DXXXX

Now, we need a way to locate the Q on a 4x4 grid (I'm not sure why the sets are necessary). I'll hazard another guess and say that the remaining Xs can represent these in binary:

DXXYY
or
DYYXX

giving you your two "coding schemes" and D tells you which one you are using.

For example
01011 means using DXXYY (as D=0) so Q is at (2,3)
or
10110 means Q is at (2,1)

NB: Co-ordinates begin at zero

Edit: It is very easy to see which set the Q is in as well by looking at the MSBs of XX and YY respectively.

carlospro7

Geee, thanks man!