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

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

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

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):-

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.	R	H	S	G	OUTPUT (F = S H)
1	0	0	0	0	1.0 = 0
2	0	0	0	1	1.0 = 0
3	0	0	1	0	0.0 = 0
4	0	0	1	1	0.0 = 0
5	0	1	0	0	1.1 = 1
6	0	1	0	1	1.1 = 1
7	0	1	1	0	0.1 = 0
8	0	1	1	1	0.1 = 0
9	1	0	0	0	1.0 = 0
10	1	0	0	1	1.0 = 0
11	1	0	1	0	0.0 = 0
12	1	0	1	1	0.0 = 0
13	1	1	0	0	1.1 = 1
14	1	1	0	1	1.1 = 1
15	1	1	1	0	0.1 = 0
16	1	1	1	1	0.1 = 0

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.

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- R	LED OF INPUT- H	LED OF INPUT- S	LED OF INPUT- R	OUTPUT
1	OFF	OFF	OFF	OFF	BULB OFF
2	OFF	OFF	OFF	ON	BULB OFF
3	OFF	OFF	ON	OFF	BULB OFF
4	OFF	OFF	ON	ON	BULB OFF
5	OFF	ON	OFF	OFF	BULB ON
6	OFF	ON	OFF	ON	BULB ON
7	OFF	ON	ON	OFF	BULB OFF
8	OFF	ON	ON	ON	BULB OFF
9	ON	OFF	OFF	OFF	BULB OFF
10	ON	OFF	OFF	ON	BULB OFF
11	ON	OFF	ON	OFF	BULB OFF
12	ON	OFF	ON	ON	BULB OFF
13	ON	ON	OFF	OFF	BULB ON
14	ON	ON	OFF	ON	BULB ON
15	ON	ON	ON	OFF	BULB OFF
16	ON	ON	ON	ON	BULB OFF

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.

List of Components
Name	Quantity
IC-7432 (LOGIC OR GATE)	1
IC-7404 (HEX INVERTER)	1
IC-7408 (LOGIC AND GATE)	4
LED	4
1K	4
100 OHM	4
BC-548 TRANSISTOR	1
5V RELAY	1
PUSH TO ON SWITCH	4
HOLDER	1
BULB	1
1N4007 DIODE	4
7805 IC	1
1000µF,63V CAPACITOR	1
0.1µF CAPACITOR	2
9V TRANSFORMER	1

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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.