How do you know if you should use 3 variables for 4 variables in IC design?

[mr_coffee]

Hello everyone, I just noticed, my IC for numbers greater then 9 to output 1, has 4 variables, why does it have to have 4 variables? couldn't I just use ABC?, because isn't 0000 == 000 and 1001 == 101, isn't 1001 9 and 101 9 also? what's the difference? I think if i just used 3 variables instead of 4 it will make the boolean expression must easier to simplfy! because then i could probably use a k-map to help me out. Here is my orginal implementation of a Boolean expression to output 1 if the number is > 9. http://img282.imageshack.us/img282/482/lastscan45vd.jpg Could this be implemented with 3 variables?

 

[faust9]

000---0
001---1
010---2
011---3
100---4
101---5
110---6
111---7
1000--8
1001--9

Counting in binary.

 

[Kenneth Mann]

You seem to be having trouble with number system representation. If a system has a base of 'nine' through 'sixteen' (Base 9 => 0 through 8) it needs four variables for representation. 101 = 5!

KM