LESSON 02 – SUM OF PRODUCTS EQUATION

LESSON WORK

QUESTION 1A

QUESTION 1B

QUESTION 2A

STEP 1

First, we determine the meaning of the inputs and outputs. Note that you may have done this differently leading to slightly different answers.

D = 0 : Dr Evil is not pressing his button

D = 1 : Dr Evil is pressing his button

G = 0 : Guard 1 is not pressing his button

G = 1 : Guard 1 is pressing his button

H = 0 : Guard 2 is not pressing his button

H = 1 : Guard 2 is pressing his button

S = 0 : Safety on (the default)

S = 1 : Safety off

L = 0 : No launch

L = 1 : Launch!

STEP 2

We now write out all possible combinations in the truth table without entering the value for L yet.

D	G	H	S	L
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1
1	0	0	0
1	0	0	1
1	0	1	0
1	0	1	1
1	1	0	0
1	1	0	1
1	1	1	0
1	1	1	1

STEP 3

The first condition

The safety (S) is OFF and Dr. Evil (D) is pressing down his button.

occurs when D=1 and S=1.

There are four rows (shown in orange) in the truth table that have D=1 and S=1. All those rows get L=1.

D	G	H	S	L
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1
1	0	0	0
1	0	0	1	1
1	0	1	0
1	0	1	1	1
1	1	0	0
1	1	0	1	1
1	1	1	0
1	1	1	1	1

STEP 4

The second condition

The safety (S) is OFF and both guards (G & H) are pressing their button.

occurs when G=1, H=1 and S=1.

There are two rows (shown in orange) in the truth table that have G=1, H=1 and S=1. Both of these rows get an L=1 value. However, the bottommost row already has L=1 as it was also covered by the first condition.

D	G	H	S	L
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1	1
1	0	0	0
1	0	0	1	1
1	0	1	0
1	0	1	1	1
1	1	0	0
1	1	0	1	1
1	1	1	0
1	1	1	1	1

STEP 5

The third condition

The safety (S) is ON and Dr. Evil (D) and both guards (G & H) are pressing their button.

occurs when D=1, G=1, H=1 and S=0.

There is only one row (shown in orange) where L is set to 1.

D	G	H	S	L
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1	1
1	0	0	0
1	0	0	1	1
1	0	1	0
1	0	1	1	1
1	1	0	0
1	1	0	1	1
1	1	1	0	1
1	1	1	1	1

STEP 6

We have covered all rows that lead to L being equal to 1. So the remaining rows have L equal to zero.

D	G	H	S	L
0	0	0	0	0
0	0	0	1	0
0	0	1	0	0
0	0	1	1	0
0	1	0	0	0
0	1	0	1	0
0	1	1	0	0
0	1	1	1	1
1	0	0	0	0
1	0	0	1	1
1	0	1	0	0
1	0	1	1	1
1	1	0	0	0
1	1	0	1	1
1	1	1	0	1
1	1	1	1	1

QUESTION 2B

We simply consider the rows that have L=1 in the truth table:

D	G	H	S	L
0	1	1	1	1
1	0	0	1	1
1	0	1	1	1
1	1	0	1	1
1	1	1	0	1
1	1	1	1	1

There are six rows with L=1 so we know our SOP equation will have 6 terms.

QUESTION 2C

Please see your teacher if you need help with the circuit diagram.