Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity. Any single variable can have a 1 or a 0 value. The complement is the inverse of a variable and is indicated by a bar over var

Boolean algebra

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, Questions
Question 1
Identify each of these logic gates by name, and complete their respective truth tables:

A A A
Output Output Output
B B B
A B Output A B Output A B Output
0 0 0 0 0 0
0 1 0 1 0 1
1 0 1 0 1 0
1 1 1 1 1 1



A A
Output Output A Output
B B

A B Output A B Output A Output
0 0 0 0 0
0 1 0 1 1
1 0 1 0
1 1 1 1



A A A
Output Output Output
B B B

A B Output A B Output A B Output
0 0 0 0 0 0
0 1 0 1 0 1
1 0 1 0 1 0
1 1 1 1 1 1

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,Question 2
Identify each of these relay logic functions by name (AND, OR, NOR, etc.) and complete their respective
truth tables:

A B A A B CR1

A B B CR1




A B Output A B Output A B Output
0 0 0 0 0 0
0 1 0 1 0 1
1 0 1 0 1 0
1 1 1 1 1 1
A CR1
A B A CR1
B
A B CR1
CR1


A B Output A B Output A Output
0 0 0 0 0
0 1 0 1 1
1 0 1 0
1 1 1 1

A
A B A B
B




A B Output A B Output A B Output
0 0 0 0 0 0
0 1 0 1 0 1
1 0 1 0 1 0
1 1 1 1 1 1

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, Question 3
The following set of mathematical expressions is the complete set of ”times tables” for the Boolean
number system:

0×0=0


0×1=0


1×0=0


1×1=1
Now, nothing seems unusual at first about this table of expressions, since they appear to be the same
as multiplication understood in our normal, everyday system of numbers. However, what is unusual is that
these four statements comprise the entire set of rules for Boolean multiplication!
Explain how this can be so, being that there is no statement saying 1 × 2 = 2 or 2 × 3 = 6. Where are
all the other numbers besides 0 and 1?
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Question 4
Boolean algebra is a strange sort of math. For example, the complete set of rules for Boolean addition
is as follows:

0+0=0


0+1=1


1+0=1


1+1=1
Suppose a student saw this for the very first time, and was quite puzzled by it. What would you say to
him or her as an explanation for this? How in the world can 1 + 1 = 1 and not 2? And why are there no
more rules for Boolean addition? Where is the rule for 1 + 2 or 2 + 2?
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