# The commutative law of addition and multiplication

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45. The commutative law of additionand multiplication indicates that:A.we can group variables in anAND or in an OR any way wewantB.anexpressioncanexpanded by multiplying termby term just the same as inordinary algebraC.the way we OR or AND twovariablesisunimportantbecause the result is the samebeD.thefactoringofBooleanexpressionsrequiresthemultiplicationofproducttermsthatcontainlikevariables46. Which of the following combinationscannot be combined into K-map groups?COMBINATIONAL LOGICANALYSIS1. Referring to the GAL diagram, whichis the correct logic function?A.𝑿 = ?? + ?̅?̅+ ??̅+ ?̅??B.𝑋 = ??̅+ ?̅?̅+ ??̅+ ???C.𝑋 = ?? + ?̅?̅+ ?̅? + ?̅??D.𝑋 = ?? + ?̅?̅+ ??̅+ ?̅??̅2. The output of an exclusive-NOR gateis 1. Which input combination is correct?A.A = 1, B = 0
INDIABIX 3B.A = 0, B = 13. The Boolean SOP expression obtainedfrom the truth table below is ________.a(n) ________.̅̅4. The 8-input XOR circuit shown has anoutputofY=1.Whichcombination below (ordered AH) iscorrect?̅?̅+ (? + ? + ?)with NOR logic, weget:inputA.10111100B.10111000C.11100111D.000111015. Implementing the expression AB +CDE using NAND logic, we get:A.(A)B.(B)C.(C)D.(D)2-input AND gateB.2-input OR gateC.Exclusive-OR gateD.None of the above6. Before an SOP implementation, theexpression𝑋 = ??(?̅? + ??)wouldrequire a total of how many gates?Toimplementtheexpression??̅?? + ???̅? + ????̅, it takes oneOR gate and ________.12457. The following waveform pattern is fora(n) ________.?̅?̅+ (? + ? + ?)with NOR logic, weget:A.(A)B.(B)C.(C)D.(D)9. A 4-variable AND-OR-Invert circuitproduces a 0 at its Y output. Whichcombination of inputs is correct??B.?̅?̅+ ?̅?C.?̅?̅+ ??D.None of these̅10. The following waveform pattern isfor a(n) ________.A.2-input AND gateB.2-input OR gateC.Exclusive-OR gateD.None of the above11.Toimplementtheexpression??̅?? + ???̅? + ????̅, it takes oneOR gate and ________.four

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Logic gate