CS 140 Lecture 6 Professor CK Cheng Tuesday 10/15/02.

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CS 140 Lecture 6 Professor CK Cheng Tuesday 10/15/02

Part I. Combinational Logic –Implementation K-map Quine-McCluskey

Quine-McCluskey Method Given F R D find min sum of products 1)Exploit the adjacency to find primes 2)Prime implicant chart

Example Id a b c d f (a,b,c,d) Given f(a,b,c,d) w/ F =  m(0,1,2,8,14) D =  m(9,10)

Corresponding 4-variable K-map f (a, b, c, d) = b’c’ + b’d’ + acd’ d a c b

Using Quine-McCluskey 1)Draw truth table that only include F and D. Order by The number of ones. Divide by regions. Id a a b b c c d d f f I II III IV

Continue again, pairing up rows from adjacent regions if they differ by exactly one bit. Put a dash where they do differ. (0,1) (0,2) (0,8) (1,9) (2,10) (8,9) (8,10) (10,14) a a b b c c d d I&II II&III III&IV

Continuing again. We stop when we can no longer combine rows. We make sure that we cover the entire onset. (0,1,8,9) (0,2,8,10) (10,14) a--1a--1 b00-b00- c0-1c0-1 d-00d-00 Primes  m(0,1,8,9)  m(0,2,8,10)  m(10,14) From here we can draw out the prime implicant chart. The top part corresponds to the onset, the side is the primes we have. Circle essential.  m(0,1,8,9)  m(0,2,8,10)  m(10,14) m0 X m1 X m2 X m8 X m14 X f(a,b,c,d) =  m(0,1,8,9) +  m(0,2,8,10) +  m(10,14) f (a,b,c,d) = b’c’ + b’d’ + acd’

Another example Id a b c d f (a,b,c,d) Given f(a,b,c,d) w/ F =  m(0,2,4,7,8,15) D =  m(9,12)

Id a a b b c c d d I II III IV V (0,2) (0,4) (0,8) (4,12) (8,9) (8,12) (7,15) a a b b c c d d (0,4,8,12)  m(0,2)  m(7,15)  m(0,4,8,12) m0 X m2 X m4 X m7 X m8 X m15 X f(a,b,c,d) =  m(0,2) +  m(0,4,8,12) +  m(7,15) f (a,b,c,d) = a’b’d + bcd + c’d’