Monday, January 19, 2015
Logic Circuits: 4-bit K-Map (Karnaugh Map) problem #1
Simplify the following function using K-map: F(w,x,y,z) = Σ(8,10,12,13,14)Solution:
This is a summation of minterms, therefore, 8, 10, 12, 13, and 14 are all 1's.
We can group the four 1's (the one's in Green) since there is only 1 bit difference from bits 00 to 10 (see figure). Please, review on Gray Code to understand better. And, we can group the two 1's (1's in Red). When dealing with minterms, an x is equal to 1 and an x' is equal to 0. Zero's will be listed as x' and one's as x.
Listing them, we get:
F = (w + w + w + w) (x + x + x' + x') (y' + y' + y + y) (z' + z' + z' + z') + (w + w) (x + x) (y' + y') (z' + z)
Now, we will simplify: w+w=w, x'+x'=x, y'+y=1
= (w + w) (x + x') (y' + y) (z' + z') + (w) (x) (y') (1)
Then, simplify further: (w)(x)(y')(1)=wxy'
= (w) (1) (1) (z') + wxy'
And, we get the answer:
F = wz' + wxy'
or
F = w(z' + xy')
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Ask a question or comment on this solution below.
God bless!:)
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