Worksheets218 Quiz 05 minterms and karnaugh maps
Total questions: 20
Worksheet time: 15mins
What is the boolean expression for the truth table below?
MN + m'n'
MN
m'n'
M+N+ m'+n"
How can two logic equations that are not identical be equal or equivalent?
They produce identical truth tables
They use the same amount of terms
They have identical inputs
They use the same amount of gates
How could you know if two boolean functions are the same
compare the circuit diagram
you can't tell
Look at the first and last gate, applying theorem 12
compare truth tables
look for identical inputs and outputs
K-Mapping is useful because...
It can be faster than Boolean simplifying
It provides a visual way to simplify terms
The answer is written simplified from directly from the map
It does not require locating a 1 to find a term
What does this k-map simplify to ?
F(X,Y) = 'x
F(X,Y) = x'y' + x'Y
F(X,Y) = (X+Y)(X+y')
F(X,Y) = x'y'
Given two inputs or variables are A and B, what should the top left cell be in a K-Map? Which mimerm is it?
a'b'
a'B
Ab'
AB
none of these
If you made a K-map for the following truth table what would be the simplified equation?
F(X,Y) = x'
F(X,Y) = x'y' + Xy'
F(X,Y) = Y+y'
F(X,Y) = (X+Y)(X+y'
Which are prime implicants
b'c'
Ad'
a'BD
Cd'
b'd'
Which are ESSENTIAL prime implicants
b'c'
Ad'
a'BD
Cd'
b'd'
Which optimal solutions
b'c' + Ad' + a'BD + Cd'
b'c' + Ad' + a'BD + b'd'
b'c' + Ad' + a'BD
b'd' + Cd'
What are the prime implicates shown on this map
AB, b'd', CD, a'c'
AB, b'd', CD, AC
BD, AB, b'd', CD, a'c'
Bc', a'D, BD, AC, Ad'
there are no valid prime implicates
What are the prime implicates that are NOT shown on this map
AB, b'd', CD, a'c'
AB, b'd', CD, AC
BD, AB, b'd', CD, a'c'
Bc', a'D, BD, AC, Ad' + b'C
there are no valid prime implicates
What prime implicates you can find on this map
a'c', b'd', ACd' , Ab'C, a'BD, Bc'D
Ac', b'd', ACd' , Ab'C, a'BD,
BD, AB, b'd', CD, ACd' , Ab'C, a'BD, Bc'D
BD, AB, b'd', CD, ACd' ,
there are no valid prime implicates
What are the ESSENTIAL prime implicates you can find on this map
a'B, a'D, BC
Ac', b'd', ACd'
a'D, BC BD,
BD, AB, a'D, BC
there are no valid prime implicates
Which are Prime Implicates for this map ?
X
Yz'
w'y'Z
DZ
BC
Which are Prime Implicates for this map ?
Xy'
w'Yz'
w'y'z
Wz'
w'XZ
Given this map (that may have issues), find the optimal solution(s) ?
WXy'z' + XWYz' + XZ + x'z'
XZ, x'z', WX, Wz'
XZ + x'z' + WX
XZ + x'z' + Wz'
XZ, x'z', Wz'
Which are Prime Implicates for this map ?
WX
YZ
w'x'y'z'
Wz'
w'XZ
Which are Prime Implicates for this map ?
XZ
WY
w'x'y'z'
Wz'
w'XZ
What is the optimal solution for this map ?
w'x'y'z' + WX + YZ
WX + YZ + WY + XZ + x'z
w'x'y'z' + WX + YZ + WY + XZ
Wz' WX + YZ + WY
WX + YZ + WY + XZ
