Combinational Logic circuit

 Combinational Logic Circuit

Basic Logic Gates Simulation

(1) AND Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the AND gate. If both inputs are "1" output is "1". Otherwise, if one input is "0" output is "0". 


(2) OR Gate - Simulation process with truth table and karnaugh map.
  • The following illustration video shows the circuit symbol and logic combinations for the OR gate. If one of input is "1" output is "1". Otherwise, if both inputs is "0" output is "0".


 
(3) NOT Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the NOT gate. If the input is "1" output is "0". Otherwise, if the input is "0" output is "1".



(4) NAND Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the NAND gate. If both inputs are "1" output is "0". Otherwise, if one input is "0" output is "1".


(5) NOR Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the NOR gate. If both inputs are "0" output is "1". Otherwise, if one input is "0" or "1" output is "0".



(6) XOR Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the XOR gate. If both inputs are the same output is "0". Otherwise, both inputs are different output is "1".


(6) XNOR Gate - Simulation process with truth table and karnaugh map
  • The following illustration video shows the circuit symbol and logic combinations for the XNOR gate. If both inputs are the same output is "1". Otherwise, both inputs are different output is "0".



Question

The top-secret recipe for making milk rice at the restaurant chain SLFC is kept in an electronic safe at their head office. The lock (L) of the safe can either be in locked or unlocked states represented by logical truth values 0 and I respectively. This lock has three different keyholes K I, K2, and K3 each with a unique key. These three keys are in the custody of the three directors of SLFC. The lock opens when at least two keys are inserted into the corresponding keyholes. The situation where the corresponding key is properly inserted into any keyhole is represented by the logical truth value 1 and all the other situations are represented by the logical truth value 0.

 (a) Construct a truth table to represent the functionality of the above alarm system.

    

(b) Derive the Boolean expression to represent the truth table constructed in the section above.

                 


(c) Simplify the Boolean expression using Boolean algebra. Clearly show all the workings and Boolean algebraic rules used for this simplification.


            










(d) Simplify the Boolean expression using Karnaugh Map.

                





(e) Construct the logic circuit for the simplified Boolean expression.



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