Thread: logic and pc design HW

Hey guys, I'm working on my Computer Architecture homework, and I'm stuck with the last problem. Here it is:

Simplify the following Boolean functions by means of a four-variable map:
F(A,B,C,D) = (Sigma)m(0,2,4,5,6,7,8,10,13,15)

I could do the smaller ones but am having problems with this thing. Any suggestions ?

thanks,

axon

http://www.valdosta.edu/~kjfamula/kmap.JPG

Use that map.

Remember to join the 1's (or 0's) in the largest possible subcubes.

the equation is F = A'B+B'D'+BD

[edit]

you can also factor out a B.

realign the equation to A'B + BD + B'D'

so...

F = B(A' + D) + B'D'


so you save a gate. k-maps do not always give you the simplest equation either.

[/edit]

A'B comes from the the horizontal row of four 1's.

B'D' comes from the upper left, bottom left, upper right, and lower right 1's (you can do this because 00 and 10 only differ by 1 bit).

BD comes from the large 2x2 cube in the center.

Hope this helps.


edit: sorry for my poor mspaint skillz =)