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10 - Use of Karnaugh Maps

 1. Karnaugh maps are similar to ______________, in that they show all possible combinations of input variables and output for a given function.

  boolean expressions

  graph based tables

  truth tables

  linked lists

 2. In a K-map, the cells are not in binary order. They are organised so that the cells next any particular one differ by just one bit.

  TRUE

  FALSE

 3. In Karnaugh maps, the variable values form the coordinates of the map (___________________) and the function output forms the squares in the map

  just the row headings

  just the column headings

  the index numbers of each row

  row and column headings

 4. In this example, for a generalised two-variable function: ______ are the variables and the function output for each combination is determined by ______
karnaughmaps_question1.png

  A and B / F

  F and A / B

  0 and 1 / abcd

  B and F / A

 5. The benefit of Karnaugh maps is that their layout enables ___________________ . A set of simplification rules for grouping can be followed to eliminate unnecessary variables

  the output 'F' to be split up into sections

  The various variables to be split up into constants

  the input 0s and 1s to both be grouped together

  output 1s to be grouped together.

 6. What would go in the blank in the karnaugh map below?
karnaughmaps_question2.png

  Ans: 0

  Ans: 2

  Ans: 1,1

  Ans: 1

 7. The following karnaugh map is for a ________________
karnaughmaps_question3.png

  OR gate

  NOR gate

  XOR gate

  AND gate

 8. In which of the following boxes(a, b, c or d) would the '0' go?
karnaughmaps_question4.png

  c

  b

  d

  a

 9. Fill in the blanks to complete the simplest boolean expression.
karnaughmaps_question5.png

  NOT A

  A

  B

  NOT B

 10. Decide whether the simplest boolean expression provided here is true (correct) or false (wrong).
karnaughmaps_question6.png

  FALSE

  TRUE

 11. Decide whether the simplest boolean expression provided here is true (correct) or false (wrong).
karnaughmaps_question7.png

  TRUE

  FALSE

 12. Under which of the following letters would 1s be placed?
karnaughmaps_question8.png

  a,b,c,d,f

  a,b,e,h

  b,c,d,e,h

  a,b,d,g

 13. Fill in the blanks in this excerpt relating to karnaugh maps.
The advantage of a Karnaugh map is that we can quickly spot the _______________ in a complicated expression. 

This advantage is more obvious when you deal with 
4 input expressions.

The only thing you must be certain of is that
every logic 1 in the map is included in at least one group

  mistaken

  logic gate simulation

  common terms

  binary sequences

 14. Analyse the karnaugh map below. Which of the following statements is accurate?
karnaughmaps_question9.png

  The simplest term obtained will be 'B' and this corresponds to the group of 0s located

  The simplest term obtained will be 'A + B' and this corresponds to the group of 1s obtained

  The group of 1s corresponds to when input A is a logic 1, which corresponds to the simplest term obtained

  The group of three 1s corresponds to when input B is a logic 1, which is the simplest term

 15. Read the excerpt on the structure of k-maps below and fill in the blanks.
It is possible to picture the map as 'wrapping around' itself. 

In essence, the right most cell differs to the left
 most cell in any row by just ____, and the top 
cell in a column differs by just _____ to the cell 
in the bottom of that column. The value contained 
in any cell is given by its row and then column value. 

  two bits

  one bit

  a '0' (never a 1)

  a single 'OR' operation

 16. Which of the following is an incorrect/inaccurate rule?
Groups may contain a maximum of two zeros
No diagonals.
Only power of 2 number of cells in each group.
Groups should be as large as possible.
Every one must be in at least one group.
Overlapping allowed.
Wrap around allowed.
Fewest number of groups possible.

  Rule 1 - grouos may not contain zeros

  All of the rules listed here are accurate and applicable.

  Rule 4 - The largest number, not fewest, of groups possible is most desirable

  Rule 2 - groups can contain diagnols

 17. Which of the following are incorrectly constructed?
Hint: 
=====
Groups must contain 1, 2, 4, 8, or in general 
2n cells. 

That is if n = 1, a group will contain two 
1s since 2 to the power of 1 = 2. 

If n = 2, a group will contain four 1's since 
2 to the power of 2 = 4
karnaughmaps_question10.png

  A and B

  C and D

  B and D

  A and D

 18. By using the rules of simplification and ringing of adjacent cells in order to ________________, the minimised result can be obtained

  duplicate as many values as possible

  make as many variables redundant

  make as many variables equal to 1

  make as many variables equal to 0

 19. Look at the karnaugh map below. Which of the following statements is true?
Statement 1
===========
The edges of the map connect up, therefore there 
is a single group of 1s, which contains the 0 and
1 values of variables A and C. These variables can 
be eliminated and the minimised result is B.

Statement 2
============
The edges of the map connect up, therefore there 
is a single group of 1s, which contains the 0 and
1 values of variables A and C. These variables can 
be eliminated and the minimised result is NOT C
karnaughmaps_question11.png

  Statement 2 is true

  Both statemnets could be true

  Neither statement is true

  Statement 1 is true

 20. Karnaugh maps also allow easy minimizations of functions whose truth tables include "don't care" conditions. A "don't care" condition is a

  condition that contains only 1s as the input

  condition that is contradictory to itself

  combination of inputs for which the designer doesn't care what the output is

  duplicate condition