3.4.2 Boolean Logic

Question 1

A computer is basically a collection of (what)?

These components have 2 states ?

Answer 1

A computer is basically a collection of transistors and circuits. These components have two states:

on - a current is flowing through the component
off - a current is not flowing through the component

Question 2

These two states can easily be represented by using binary:

Answer 2

These two states can easily be represented by using binary:

1 = on (TRUE)
0 = off (FALSE)

Question 3

In its most basic form, a computer is ?

A logic gate is ?

Answer 3

In its most basic form, a computer is a collection of powered and unpowered circuits and transistors.

A logic gate is a series of transistors connected together to give one or more outputs, each output being based on the input or combination of inputs supplied to it.

Question 4

NOT Logic gate

• symbol
• expression operator (statement)

Answer 4

Triangle pointing to circle
—|>0—

A¯ (The line would be above)

Question 5

AND Logic gate

• symbol
• expression operator (statement)

Answer 5

D shape
=D—

A.B (A dot B)

Question 6

OR Logic gate

• symbol
• expression operator (statement)

Answer 6

Crescenty shape - but slightly stretched horizontally
=) >-

A+B

Question 7

XOR Logic gate

• symbol
• expression operator (statement)

Answer 7

OR gate, but with another end of crescent

=)) >-

A⊕B (A plus B with a circle around the plus)

Question 8

NOT gate truth table

Answer 8

Input Output
1 0
0 1

Question 9

AND gate truth table

Answer 9

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

Question 10

OR gate truth table

Answer 10

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

Question 11

XOR gate is also called

Answer 11

Exclusive OR gate

Question 12

XOR gate truth table

Answer 12

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

Question 13

Q = A.B (WITH A LINE OVER WHOLE THING)

How to draw

Answer 13

AND gate followed by a NOT gate

Question 14

The convention for truth table?

Answer 14

The convention for truth tables is that the rightmost column of inputs goes 0101010101…., and then each column left doubles the intervals of 0s and 1s
Like this:

Input A	Input B
0	0
0	1
1	0
1	1

If there were a third input, the rows would go 0 0 0 0, then 1 1 1 1 if needed. A fourth would have up to eight 0s, then switch to eight 1s if needed, and so on

Question 15

If three inputs - how many rows will truth table have ?

Answer 15

We know from the start that the truth table will have 8 rows because there are 8 possible combinations of 3 inputs. (2 x 2 x 2 = 8)