Topic-03 Answers - Computer organisation and Architecture PDF

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Topic-03 Practice Questions Q0 1 Construct a truth table for the following: xy z+x ( y z ) ' +( xy z ) ' Sum(x, y, z) = xyz + x(yz)' + (xyz)'

Q0 2 Co n s t r u c tat r u t ht a b l ef o rt hef o l l owi n gl o gi c a le x p r e s s i o n : ( x+y ) ( x+z ) ( x ' +z )

Q0 3 Using DeMorgan's Law, write an expression for the complement of Fif F( x , y , z )= x ( y ' +z )

Q0 4 Us i n gDe Mo r g a n ’ sLa w, wr i t ea ne x pr e s s i o nf o rt h ec o mp l e me n tofFi f : F(x,y,z) = xy + x‘z + yz‘

Q0 5 Using the basic identities of Boolean algebra, show that: x ( x ' +y )=x y

Q0 6 Simplify the following functional expressions using Boolean algebra and its identities. x y+x y '

Q0 7 Use any method (ie. identities or truth table) to prove the following either True for False. y z+x y z ' +x ' y ' z=x y+x ' z

Q0 8 The truth table for a Boolean expression is shown below. Write the Boolean expression in sumof-products form:

Q0 9 Dr a wt het r u t ht a b l ea n dr e wr i t et h ee x pr e s s i o nb e l o wa st hec o mp l e me n ts u mo ft wop r o d uc t s : xz’ + y’z + x’y

Q1 0 Given the function: F( x , y , z ) =x y ' z+x ' y ' z+x y z a. List the truth table for F

b.

Draw the logic diagram using the original Boolean expression

c.

Simplify the expression using Boolean algebra and identities

d.

List the truth table for your answer in part c

e. Draw the logic diagram

Q-11 Find the truth table for the following logic circuit

Q-12 Find the truth table for the following circuit

Q1 3 Dr a wt hec o mb i na t i o na lc i r c u i tt h a td i r e c t l yi mp l e me n t st h ef ol l o wi n gBo ol e a ne x p r e s s i o n :

F( x, y , z )=x ' yz+yz+xy '

Q1 4 Design a circuit with three inputs (x , y ,and z ) representing the bits in a binary number, and three outputs (a , b ,and c ) also representing bits in a binary number. When the input is 0, 1, 2 or 3, the binary output should be one less than the input. When the binary input is 4,5,6, or 7, the binary output should be one greater than the input. Show your truth table, all computations for simplification and the final circuit. Q1 5 Write a Boolean function and design a logic circuit, use of basic logic gates to activate a speed camera during morning 7.00 am to 10.00 am and afternoon 1.00 pm to 3.00 pm. You need to use 24 hour clock timing when designing this circuit. Q1 6 Write a Boolean function and design a logic circuit, use of basic logic gates to activate a boom gate for a car park. The car park will be used during the months February, April, July, September and December....