13-04-2013, 04:20 PM
IMPLEMENTATION OF BOOLEAN FUNCTION
AIM
To simplify the Boolean expression using Karnaugh Map technique and implement the
logic circuit using digital logic gates.
THEORY:
The simplification of the switching functions using boolean laws and theorems becomes
complex. With the increase in the number of variables and terms, the Karnaugh Map technique
provides a systematic method for simplifying and manipulating switching expressions. In this
technique, the information contained in a truth table or available in the POS or SOP form is
represented on the Karnaugh Map (K-Map). The K-Map is actually a modified form of a truth
table. Here, the combinations are conveniently arranged to aid the simplification process by
applying the rule Ax Ax A. In an n variable K-Map, there are 2n cells. Each cell corresponds
to one combination of n variables. Therefore, for each row of the truth table, i.e. for each min
term and for each max term, there is one specific cell in the K-Map. The decimal code
corresponding of variables are given inside the right top corner of each cell. The variables have
been marked as A,B,C, D and E, and the binary numbers formed by them are taken as AB, ABC,
ABCD and ABCDE for 2,3,4 and 5 variable respectively.
PROCEDURE:
1. Draw the Karnaugh Map for the given expression.
2. Simplify the Karnaugh Map and obtain the minimal boolean expression.
3. Draw the logic diagram for the simplified expression using basic gates.
4. Formulate the truth table for the logic diagram.
5. Connections are given as per the circuit diagram on the bread board.
6. The power supply is switched ON and set a voltage of 5 Volts.
7. If the input to be given to a gate is logic ‘1’ then it is connected to +5 Volts and if the input to be given to the gate is logic ‘0’ then the particular input terminal is connected to ground.
8. Truth table is verified.
9. If the output is logic ‘1’ then the LED glows, if the output is logic ‘0’ then the LED does not glow.