Transcript Combinational Circuit Design Problem 1 Solution

Combinational Circuit Design
• A combinational circuit consists of logic gates.
• It processes the input signals (coming from an
external source) to produce the output
signals (to an external destination).
•All signals are binary, i.e., either a logic 0 or a
logic 1.
Combinational Circuit Design
• All signals may have 1 or 2 lines.
– If 1 line, represents either the normal
(unprimed) variable or the complement
(primed).
– If 2 lines, both primed and unprimed variables
are represented. It is assumed that one is
always the complement of the other.
– Unless stated, it shall be assumed that 2 lines
are available for each of the input signals.
Design Procedure
1. Problem Statement
– The specification is normally in plain language
explaining how the circuit is supposed to
function.
– The designer needs to rely on intuition and
experience to arrive at the correct
interpretation of the problem.
Design Procedure
2. Problem Analysis
– Identify the inputs and the outputs.
– Assign variables to the inputs and outputs.
– Determine the relationship between the
inputs and the outputs. This can either be in
the form of a truth table showing the
relationship, or a simple Boolean expression
derivable from the problem.
Design Procedure
3. Logic Circuit Design
– Simplify the Boolean expression.
» Boolean Algebra
» Karnaugh Map
– Draw the corresponding logic diagram.
Combinational Circuit Design Problem 1
Problem
The Last Rogue's Bank wants to set up a simple
security system. This is to be connected directly
to an alarm at the Police Station for immediate
response. There shall be a switch (T) at the
teller's window to trigger the alarm when a
robbery is in progress. After the bank closes, a
main switch (M) shall be turned on to enable the
sensors within the bank. One sensor shall be
placed on the only door into the bank (D). This
shall trigger the alarm when the door is opened if
the main switch is on unless a secret outside
switch (S) is turned on by a special key.
Combinational Circuit Design Problem 1
Another sensor shall be placed on the vault door
(V). This shall trigger the alarm when the vault is
opened if the main switch is on. The bank
president shall have a switch by his desk (P)
which when turned on by his key will disable the
security system. This is in case the president
wants to rob the bank himself. Design a
combinational logic circuit which will generate
the signal (A) that will turn on the police station
alarm as specified above.
Combinational Circuit Design Problem 1 Solution
Solution
– Input
T
M
D
S
V
P
signals
Teller's switch
Main switch
Front door sensor
Secret outside switch
Vault door sensor
President's switch
Combinational Circuit Design Problem 1 Solution
– Output signal
A
Police station alarm
– When does the alarm go off?
» If one of the following conditions is
satisfied:
•Teller turns on switch (T).
•Front door opens when main switch is on
and secret outside switch is off (DM S).
•Vault door is opened when main switch is
on and president's switch if off (VM).
» Unless the president's switch if turned on.
Combinational Circuit Design Problem 1 Solution
• Output function
A  (T  DM S  VM )P
• Circuit Diagram