Homework 4 KEY Fall 2014 CDA3103 PDF

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CDA 3103

Fall 2014

CDA 3103 Computer Organization Homework #4 Solution Set 1

Problems

In this solution set, nagation or NOT of x is denoted by x′ instead of x. p26 in 3rd edition and p28 in 4th edition 26. Construct the XOR operator using only AND, OR and NOT gates. Ans. x XOR y = x'y + xy'

p27 in 3rd edition and p29 in 4th edition *27. Construct the XOR operator using only NAND gates. Hint: x !"# y = ((x ' y)' (xy' )' )'$ Ans.

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Homework

CDA 3103

Fall 2014

Homework

p38 in 3rd edition and p42 in 4th edition

38. Assume you have the following truth tables for functions F1(x,y,z) and F2(x,y,z):

! x

y

z

F1

F2

0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1

1 1 1 0 0 0 0 0

0 0 1 1 0 0 1 1

a. Express F1 and F2 in sum-of-products form. b. Simplify each function. c. Draw one logic circuit to implement the above two functions. Ans. a. "#(x,y,z) = x'y'z' + x'y'z + x'yz' and "$(x,y,z) = x'yz' + x'yz + xyz' + xyz b. "#(x,y,z) = x'y' + x'z' and "$(x,y,z) = y c. Final circuit not drawn

p40-41 in 3rd edition and p44-45 in 4th edition

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CDA 3103

Fall 2014

Homework

40. Design a truth table for a combinational circuit that detects an error in the representation of a decimal digit encoded in BCD (this circuit should output a 1 when the input is one of the six unused combinations for BCD code). Ans. w

x

y

z

F1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1

___________________________________________________________________________ 41. Simplify the function from Exercise 40 and draw the logic circuit. Ans. F = wx + wy!

p51 in 3rd edition and p54 in 4th edition 51. Complete the truth table for the following sequential circuit:

Ans. X 0 0 0 0 1 1 1 1

Y 0 0 1 1 0 0 1 1

Z(Q) 0 1 0 1 0 1 0 1

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Next State S C(Q) 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1

CDA 3103

Fall 2014

Homework

1. Draw the combinational circuit that directly implements the following Boolean expression: F (x, y, z) = x + xy + y′ z

 2. Find the truth table that describes the following circuit:

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CDA 3103

Fall 2014

Homework

Ans.

  

x        

y        

z        

3. How many inputs does a decoder have if it has 32 outputs? answer: 5 inputs. 4. How many control lines does a multiplexer have if it has 16 inputs? answer: 4 control inputs.

5

F        ...