Sunday, June 16, 2024

Verification Of K-Map Technique (KARNAUGHMAP) By Multi-Password Operated Electrical Gadget

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The karnaugh map i.e. K-map method is a graphical technique to simplifying Boolean expressions. It is a diagrammatic technique which is used to reduce the Boolean expression .K-maps are also known as 2d truth tables. We use the K-map for functions with number of variables i.e. 2-variable k-map,4-variable k-map etc.,it’s basically depends on the number of variable in the Boolean expression. There are two kind of Boolean expression i.e. SOP (sum of product) and POS (product of sum).Here we verify the concept of K-map using SOP expression.

Let our Boolean expression is:

Here in this Boolean expression we have 4-variable i.e. R, H,S and G.So we require 4-variable K-map. The total number of cell in a K-map depends on the no. of variable.

Total no. of cell in a K-map = 2^no.of variable

Here we have 4 variable so total no. of cell = 2^4 =16

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The format of 4-variable K-map is shown in Fig(1):-

Fig. 1

Now according to our Boolean expression we put 1 in corresponding cell. For our Boolean expression we put 1 in corresponding cell as in Fig. (2):-

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Fig. 2

So here we find a group of four 1’s so we use this group and find out the minimize expression as in Fig.(3):-

Fig. 3

Here the Simplification Is F = S H

Now we create a truth table for the ouput depends on the 4-variable input values, here inputs are R, H, S and G and output is F.

SR.NO.RHSGOUTPUT (F = S H)
100001.0 = 0
200011.0 = 0
300100.0 = 0
400110.0 = 0
501001.1 = 1
601011.1 = 1
701100.1 = 0
801110.1 = 0
910001.0 = 0
1010011.0 = 0
1110100.0 = 0
1210110.0 = 0
1311001.1 = 1
1411011.1 = 1
1511100.1 = 0
1611110.1 = 0
Table 1

Now we prove it via designing a prototype.Our Boolean expression was :

Here for 4-inputs we use 4-push to on switches and to indicate the value of each inpuit we use a corresponding LED as in fig.4. LED Glow means 1 and LED OFF means 0.

Fig. 4

So after designing the above prototype, Here As Par The Connection Of Different IC’s We Will Find The Output(The Output Here Will Be Amplified First Via NPN Transistor And Then Apply To Drive A Relay So As To Drive Ac Bulb)As Represent In Table we find the following result(TABLE-2):

SR.NO.LED OF INPUT- RLED OF INPUT- HLED OF INPUT- SLED OF INPUT- ROUTPUT
1OFFOFFOFFOFFBULB OFF
2OFFOFFOFFONBULB OFF
3OFFOFFONOFFBULB OFF
4OFFOFFONONBULB OFF
5OFFONOFFOFFBULB ON
6OFFONOFFONBULB ON
7OFFONONOFFBULB OFF
8OFFONONONBULB OFF
9ONOFFOFFOFFBULB OFF
10ONOFFOFFONBULB OFF
11ONOFFONOFFBULB OFF
12ONOFFONONBULB OFF
13ONONOFFOFFBULB ON
14ONONOFFONBULB ON
15ONONONOFFBULB OFF
16ONONONONBULB OFF
TABLE 2

Now When we compare the table(1) and table(2) results than we find that both are equal[NOTE:-LOGIC 1 in table(1)and BULB ONin table (2) are same and LOGIC 0 in table(1)and BULB OFF in table 2 are same].So finally we prove the K-map verification technique by designing a prototype.

This prototype can be used at our home for controlling electrical appliance by using more than one password .Like here to switch on the output AC BULB we need one password which is any one among four passwords as in sr.no.5, sr.no.6, sr.no.13 and sr.no.14.

Author’s Prototype
List of Components
NameQuantity
IC-7432 (LOGIC OR GATE)1
IC-7404 (HEX INVERTER)1
IC-7408 (LOGIC AND GATE)4
LED4
1K4
100 OHM4
BC-548 TRANSISTOR1
5V RELAY1
PUSH TO ON SWITCH4
HOLDER1
BULB1
1N4007 DIODE4
7805 IC1
1000µF,63V CAPACITOR1
0.1µF CAPACITOR2
9V TRANSFORMER1
Table 3:- List of components use in project

RAKESH JAIN received Master degree in VLSI, B.E. in electronics and communication, DIPLOMA in electronics. He is currently working as an Assistant professor in ECE department in Geetanjali institute of technical studies, Udaipur. His research area is SENSOR and Microcontroller. He has 26 copyright and 3 Indian patents. He has also been honored with Mewar Scientist Award2023.

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