Question

introduction to HDL, 

1. Logic Circuits. Draw the equivalent logic circuit diagram of the given expression. 

F = (ab)

̅̅̅̅̅̅ + (ac)

2. Truth Table. Provide the truth table from your logic circuit in part 1. 

3. K-Mapping. Simplify the circuit using the truth table you derived from part 2. 

4. Back to Logic Circuits. Draw the equivalent logic circuit diagram of your simplified expression from

part 3. 

Answer 1

1. Logic Circuits: The given expression is F = (ab) ̅̅̅̅̅̅ + (ac). Let's draw the equivalent logic circuit diagram for this expression:

luaCopy code        ----
       |    |
 a ----|    |---- AND ---- F
       |    |        ----
         |
        NOT
         |
 b ----|    |
       |    |        ----

         |
 c ----|    |
       |    |        ----

In this circuit diagram, 'AND' represents the logical AND gate, and 'NOT' represents the logical NOT gate. The inputs 'a' and 'b' are connected to the first AND gate, and the output of this AND gate is connected to the NOT gate. The input 'c' is connected directly to the second AND gate. The outputs of both AND gates are then connected to the inputs of the OR gate, which represents the overall expression F.

2. Truth Table: To derive the truth table for the given logic circuit, we need to consider all possible combinations of inputs 'a', 'b', and 'c'. Let's assume '0' represents logic 'false' and '1' represents logic 'true'.

The truth table for the logic circuit is as follows:

cssCopy code| a | b | c | F |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |

3. K-Mapping: Based on the truth table, we can now simplify the circuit using Karnaugh maps (K-maps). The K-map for the given expression F is as follows:

luaCopy code   c\ab | 00 | 01 | 11 | 10 |   ------|----|----|----|----|
     0   |  1 |  0 |  1 |  0 |     1   |  0 |  0 |  1 |  1 |

From the K-map, we can see that there are two groups of adjacent '1's. One group corresponds to the term (ab) ̅̅̅̅̅̅ and the other group corresponds to the term (ac).

4. Back to Logic Circuits: Now, let's draw the equivalent logic circuit diagram for the simplified expression obtained from the K-map:

luaCopy code           ----
          |    |
 a ------->| OR |---- F
          |    |           ----
            |
 b ------->|    |
          |    |           ----
            |
 c ------->|    |
          |    |           ----

In this simplified circuit, there are two inputs 'a' and 'c' connected to the OR gate directly, and the input 'b' is connected to the OR gate through a NOT gate. The output of the OR gate represents the simplified expression from part 3.