# 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

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

the index numbers of each row

4. In this example, for a generalised two-variable function: ______ are the variables and the function output for each combination is determined by ______ 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? Ans: 0

Ans: 2

Ans: 1,1

Ans: 1

7. The following karnaugh map is for a ________________ OR gate

NOR gate

XOR gate

AND gate

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

b

d

a

9. Fill in the blanks to complete the simplest boolean expression. NOT A

A

B

NOT B

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

TRUE

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

FALSE

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