Converting Analog Signals to Digital: A 2-bit A/D System

[Beeorz]

Obtain the digital words corresponding to the indicated analog signal levels, a through j, as shown in Figure P8.38, that would be assigned by an A/D system with 2 bits.

http://img256.imageshack.us/f/eehmrw1.png/

a. None of the above
b. a=11, b=01,c=10,d=01, and e=01
c. a=11,b=10,c=01,d=01, and e=10
d. a=00,b=10,c=01,d=10, and e=10


I understand what the position and weight of the digit imply but for some reason no matter how I look at this problem I cannot seem to make sense of it.

Any help would be greatly appreciated.

 

[cepheid]

I suppose it depends upon what the rules you're using for digitization are, but given that two bits can only result in four distinct digital signal levels, and given that the original analog signal levels range between 0 and 15, it would seem to make sense to divide that range into four intervals -- everything in the lowest interval gets assigned 00, et cetera.

 

[Beeorz]

Okay, that makes sense.

Now if I was using signal levels a through e only:

~The range would be from 0 to 10 and have 4 zones.
~Thus 10/4 = 2.5

~00 is 0-2.5
~01 is 2.5-5
~10 is 5-7.5
~11 is 7.5-10

If that is all correct then the answer would indeed be A because:

a=00
b=01
c=11
d=10
e=01