Chapter 18 Boolean Algebra and Logic Circuits

Question 1

Which is the sign in boolean algebra for AND?

Answer 1

. for example: A.B is A AND B

Question 2

Which is the sign in boolean algebra for OR?

Answer 2

+ for example: A+B is A OR B

Question 3

Which is the sign in boolean algebra for NOT?

Answer 3

̅ for example: ̅A is NOT A

Question 4

How do you write the Identity/Law identity in both forms?

Answer 4

AND form: 1.A = 1

OR form: 0+A = A

Question 5

How do you write the Identity/Law Null in both forms?

Answer 5

AND form: 0.A = 0

OR form: 1+A = 1

Question 6

How do you write the Identity/Law Idempotent in both forms?

Answer 6

AND form: A.A = A

OR form: A+A = A

Question 7

How do you write the Identity/Law Inverse in both forms?

Answer 7

AND form: A.A ̅ = 0

OR form: A+A ̅ = A

Question 8

How do you write the Identity/Law Commutative in both forms?

Answer 8

AND form: B.A = A.B

OR form: A+B = B+A

Question 9

How do you write the Identity/Law Associative in both forms?

Answer 9

AND form: (A.B).C = A.(B.C)

OR form: (A+B)+C = A+(B+C)

Question 10

How do you write the Identity/Law Distributive in both forms?

Answer 10

AND form: A+B.C = (A+B) (A+C)

OR form: A.B+C = (A+B) (A+C)

Question 11

How do you write the Identity/Law Absorption in both forms?

Answer 11

AND form:A.(A+B) = A

OR form:A+A.B = A

Question 12

How do you write the Identity/Law De Morgan’s law in both forms?

Answer 12

AND form:(A.B) ((A.B)) ̅= A ̅+B ̅

OR form:((A+B)) ̅ = A ̅.B ̅

Question 13

How do you write the Identity/Law Double complement in both forms?

Answer 13

In both forms: TWO LINES OVER A = A or NOT NOT A = A

Question 14

What needs to happen for a carry bit to be 1 in a half adder?

Answer 14

Both inputs have to be TRUE or 1

Question 15

What happens in a half adder if only one of the inputs is 1?

Answer 15

The output will be 1 and 0.

Question 16

What happens in a half adder neither of the inputs is 1?

Answer 16

The output will be 0 and 0.

Question 17

How does a half adder circuit constructed from NAND gates look like?

Answer 17

https://www.tutorialspoint.dev/computer-science/digital-electronics-and-logic-design/half-adder-half-subtractor-using-nand-nor-gates -> the site on which the Logic circuit can be seen

Question 18

How does a half adder circuit constructed from NAND gates look like?

Answer 18

https://www.tutorialspoint.dev/computer-science/digital-electronics-and-logic-design/half-adder-half-subtractor-using-nand-nor-gates -> the site on which the Logic circuit can be seen

Question 19

How many inputs are in a full adder?

Answer 19

3

Question 20

What happens in a full adder if none of the inputs is 1?

Answer 20

The output will be 0 0

Question 21

What happens in a full adder if one of the inputs is 1?

Answer 21

The output will be 1 0

Question 22

What happens in a full adder if two of the inputs is 1?

Answer 22

The output will be 0 1

Question 23

What happens in a full adder if all three of the inputs is 1?

Answer 23

The output will be 1 1

Question 24

What does combinational circuit mean?

Answer 24

A combinational circuit is a circuit in which the output is only dependent on the input

Question 25

What does sequential input mean?

Answer 25

A sequential circuit means a circuit in wich the output depends on the input values and the previous output.

Question 26

Which are the three stages in a truth table when calculating the final output?

Answer 26

Input values, Initial state and final output.

Question 27

How does a SR flip-flop circuit made of NOR gates look like?

Answer 27

https://electronics.stackexchange.com/questions/163164/sr-flip-flop-nor-or-nand -> the site

Question 28

How does a SR flip-flop circuit made of NOR gates look like?

Answer 28

https://www.electronicshub.org/sr-flip-flop-design-with-nor-and-nand-logic-gates/ -> the site

Question 29

Why does a JK flip flop have a clock?

Answer 29

To synchronize the inputs.

Question 30

What can be the outputs in a JK flip flop?

Answer 30

00 = Q unchanged
10 = 1
01 = 0
11 = Q toggles

Question 31

How to make a boolean algebra representation of a circuit by sum-of-product method?

Answer 31

First make a truth table and write down the rows that have a true output.
example: W = A.B + A ̅.B ̅

Question 32

How is each cell in a karnaugh map structured?

Answer 32

Each cell in a Karnaugh map shows the value of the output X for a combination of input values for A and B or of the other inputs.