# Combinational logic

Discussion in 'Homework Help' started by jmabait1, Feb 15, 2011.

1. ### jmabait1 Thread Starter New Member

Feb 15, 2011
2
0
Design a circuit to implement that seat beat alarm that is required on all cars. A set of sensor switches is available to supply the inputs to the onboard computer. One switch will be turned on if the key is inserted. A switch is placed under each front seat and will turn on if someone sits in the cooresponding seat. Finally, a switch is attached to each front seat which will turn on if and only if that seat belt is fastened. An alarm buzzer is to sound when the key is insered in the ignition, providing that either of the front seats is occupied and the cooresponding seat belt is not fastened.

Inputs:

Ignition - A (goes high when key inserted, goes low when key not inserted)
Left front seat - B (high when seat occupied, low when seat empty)
Right front seat - C (high when seat occupied, low when seat empty)
Left seat belt - D (high when belt fastened, low when belt not fastened)
Right seat belt - E (high when belt fastened, low when belt not fastened)

Output
Alarm - Z (alarm sounds when level is high, alarm is silent when level is low)
----------------------------------------------------------------

i don't know if this is right:

A B C D E Z
1 0 0 0 0 0
1 0 0 0 1 0
1 0 0 1 0 0
1 0 0 1 1 0
1 0 1 0 0 1
1 0 1 0 1 0
1 0 1 1 0 1
1 0 1 1 1 0
1 1 0 0 0 1
1 1 0 0 1 1
1 1 0 1 0 0
1 1 0 1 1 0
1 1 1 0 0 1
1 1 1 0 1 1
1 1 1 1 0 1
1 1 1 1 1 0

(') = inverse

how to do you DeMorganize this equation:
( ' ) = inverse

Z = A B' C D' E + A B' C D E' + A B C' D' E' + A B C' D' E + A B C D' E' + A B C D' E + A B C D E'
= A B' C D' E + A C D E'(B' + B) + A B C' D' (E' + E)+ A B C D' (E' + E)
= A B' C' D' E + A C D E' + A B C' D' + A B C D'
= A B' C' D' E + A C D E' + A B D' (C' + C)
= A B' C' D' E + A C D E' + A B D'

2. ### Georacer Moderator

Nov 25, 2009
5,142
1,266
Were you taught about Karnaugh Maps? If so, you need to simplify the expression, taking into account, only the variable B,C,D and E. The Ignition signal can be incorporated afterwards, with an AND gate along with the output of the Boolean function.

Here's a link for the K-maps: