Notes 3 Flashcards
any logical function can be broken down into the ____ of its rows
sum
minterms
m0, m1, m2,…
A B C | F
0 0 0 ….m0
0 0 1 … m1
0 1 0 … m2
.
.
.
we can write any arbitrary function in ____ _ notation
little m
write the following function in little m notation:
F = AC’ +BC’
F = m2 +m4+m6
or
F = Σ m(2,4,6)
write the equation for a two-variable function G = Σ(0,1)
G = A’B’ + A’B
= A”
technique to do simplification of the sum of products
k maps
k maps for two variables
A\B
\ 0 1
0 m0 m1
1 m2 m3
2 by 2 grid
k maps for three variables
A\B C
\
00 01 11 10
0 m0 m1 m3 m2
1 m4 m5 m7 m6
k maps for 4 variables
AB\CD
\
00 01 11 10
00 m0 m1 m3 m2
01 m4 m5 m7 m6
11 m12 m13 m15 m14
10 m8 m9 m11 m10
gray code
one bit flipped each time
rules for legal circles on a K map
must be powers of 2 (ie 2^0, 2^1, 2^2, …, 2^n
must be contiguous (touching each other)
should be as large as possible
cannot include zeros
the circles can overlap
how do you get the simplified equation from the kmap
add all the circles together
implicant
a circle
prime implicant
as big of a circle as you can draw
essential prime implicant
the biggest circle you can draw with at least one non overlapping 1
