Advanced Karnaugh Maps Quiz � Multi-Variable and Don�t-Care Simplification (MP.1, MP.7)

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1) F(W,X,Y,Z)=Σm(0,2,8,10)F(W,X,Y,Z)=\Sigma m(0,2,8,10)F(W,X,Y,Z)=Σm(0,2,8,10). Minimal SOP:

W′Y′+W′YW'Y' + W'YW′Y′+W′Y

W′Z′+W′ZW'Z' + W'ZW′Z′+W′Z

W′X′W'X'W′X′

X′Z′X'Z'X′Z′

Minterms 0,2,8,10 share W=0W=0W=0 and X=0X=0X=0 (vary Y,ZY,ZY,Z) → group of 4 → W′X′W'X'W′X′.

Explanation

Minterms 0,2,8,10 share W=0W=0W=0 and X=0X=0X=0 (vary Y,ZY,ZY,Z) → group of 4 → W′X′W'X'W′X′.

About This Quiz

Karnaugh Maps For Advanced Logic Minimization - Quiz

Take simplification to the next level! This quiz challenges you with advanced Karnaugh map problems requiring careful grouping and insight. Try this quiz to push your Boolean algebra skills.

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2) Which is a valid wrap-around group in a 4-var K-map?

Four corners

First and last columns

First and last rows

All of the above

Both rows and columns wrap, and the four corners are pairwise adjacent.

Explanation

Both rows and columns wrap, and the four corners are pairwise adjacent.

3) If a map has few 1’s and many 0’s, which form is simpler?

SOP

POS

Both same

Neither

With few 1’s, grouping 1’s (SOP) usually yields fewer/larger groups.

Explanation

With few 1’s, grouping 1’s (SOP) usually yields fewer/larger groups.

4) F(W,X,Y,Z)=Σm(1,3,5,7)F(W,X,Y,Z)=\Sigma m(1,3,5,7)F(W,X,Y,Z)=Σm(1,3,5,7), d={9,13}d=\{9,13\}d={9,13}. Minimal SOP:

X′ZX'ZX′Z

W′ZW'ZW′Z

YZY ZYZ

W′X′ZW'X'ZW′X′Z

Ones at all odd minterms. Using don’t-cares forms 4-groups where Y=1Y=1Y=1 and Z=1Z=1Z=1 → YZYZYZ.

Explanation

Ones at all odd minterms. Using don’t-cares forms 4-groups where Y=1Y=1Y=1 and Z=1Z=1Z=1 → YZYZYZ.

5) If a minterm is covered by only one prime implicant, that PI is:

Redundant

Essential

Non-essential

Don’t-care

By definition, it’s essential.

Explanation

By definition, it’s essential.

6) Which minimal form has fewer literals? Given F=A′B+AB′F = A'B + AB'F=A′B+AB′ vs F=A⊕BF = A \oplus BF=A⊕B (XOR).

First has fewer

Second has fewer

Same

Depends

Literal count counts variables in products. XOR is shorthand; in sum-of-products it’s two 2-literal terms.

Explanation

Literal count counts variables in products. XOR is shorthand; in sum-of-products it’s two 2-literal terms.

7) F=Σm(0,1,2,3,8,9,10,11)F=\Sigma m(0,1,2,3,8,9,10,11)F=Σm(0,1,2,3,8,9,10,11). Minimal SOP:

W′X′W'X'W′X′

W′W'W′

X′X'X′

W′+X′W' + X'W′+X′

All minterms where W=0W=0W=0 regardless of others → whole top half groups to W′W'W′.

Explanation

All minterms where W=0W=0W=0 regardless of others → whole top half groups to W′W'W′.

8) Two disjoint 4-groups covering all 1’s always give the unique minimal solution.

True

False

Different combinations of valid groups can yield equally minimal solutions.

Explanation

Different combinations of valid groups can yield equally minimal solutions.

9) For FFF with 0’s at M(4,5,6,7)M(4,5,6,7)M(4,5,6,7) only, minimal POS is:

X′+Y′X' + Y'X′+Y′

W+XW + XW+X

YYY

X+YX + YX+Y

The 0’s (a 4-block with X=1X=1X=1 or Y=1Y=1Y=1) yield a single maxterm → F=(X+Y)′F = (X + Y)'F=(X+Y)′' so minimal POS is X+YX + YX+Y.

Explanation

The 0’s (a 4-block with X=1X=1X=1 or Y=1Y=1Y=1) yield a single maxterm → F=(X+Y)′F = (X + Y)'F=(X+Y)′' so minimal POS is X+YX + YX+Y.

10) Over-minimizing by avoiding overlap can cause static hazards.

True

False

Overlap can help reduce hazards by keeping coverage during signal changes (implementation detail, but good practice insight).

Explanation

Overlap can help reduce hazards by keeping coverage during signal changes (implementation detail, but good practice insight).

11) F(A,B,C)=ΠM(0,2,4,6)F(A,B,C)=\Pi M(0,2,4,6)F(A,B,C)=ΠM(0,2,4,6) (zeros at even indices). Minimal POS is:

A+CA + CA+C

A′+C′A' + C'A′+C′

B′+C′B' + C'B′+C′

B+CB + CB+C

Even minterms correspond to C=0C=0C=0 when B=1B=1B=1 pattern; grouping 0’s gives B+CB + CB+C as a single clause in POS.

Explanation

Even minterms correspond to C=0C=0C=0 when B=1B=1B=1 pattern; grouping 0’s gives B+CB + CB+C as a single clause in POS.

12) On a 4-variable K-map, which group sizes are valid?

Any number of adjacent 1’s

Only 1 and 2

Any power of 2 (1,2,4,8,16)

Only 4 and 8

Valid groups are powers of two to keep variables consistent.

Explanation

Valid groups are powers of two to keep variables consistent.

13) Which product term covers exactly the 4-cell block where W=1W=1W=1 and X=0X=0X=0 (any Y,ZY,ZY,Z)?

W′XW'XW′X

WX′WX'WX′

W′X′W'X'W′X′

WXWXWX

W=1⇒WW=1\Rightarrow WW=1⇒W, X=0⇒X′X=0\Rightarrow X'X=0⇒X′. Term WX′WX'WX′ spans a 4-cell block across Y,ZY,ZY,Z.

Explanation

W=1⇒WW=1\Rightarrow WW=1⇒W, X=0⇒X′X=0\Rightarrow X'X=0⇒X′. Term WX′WX'WX′ spans a 4-cell block across Y,ZY,ZY,Z.

14) Best use of don’t-cares is to:

Always include

Always exclude

Include them only if they make larger valid groups

Use them to cover uncovered 0’s

Treat X as 1 only when it enlarges a group, simplifying the function.

Explanation

Treat X as 1 only when it enlarges a group, simplifying the function.

15) F(W,X,Y,Z)=Σm(0,2,3,8,10,11)F(W,X,Y,Z)=\Sigma m(0,2,3,8,10,11)F(W,X,Y,Z)=Σm(0,2,3,8,10,11). Minimal SOP is:

W′X′+W′YZW'X' + W'YZW′X′+W′YZ

W′X′+W′YW'X' + W'YW′X′+W′Y

X′Z′+W′YX'Z' + W'YX′Z′+W′Y

W′+X′Z′W' + X'Z'W′+X′Z′

Group {0,2,8,10}\{0,2,8,10\}{0,2,8,10} → W′X′W'X'W′X′ (varies Y,ZY,ZY,Z). Group {3,11}\{3,11\}{3,11} (wrap in column) → W′YW'YW′Y. Combined minimal SOP: W′X′+W′YW'X' + W'YW′X′+W′Y.

Explanation

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Cierra Henderson |MBA |

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.

Karnaugh Maps for Advanced Logic Minimization