Función Lógica: Tabla de verdad y Circuito Combinacional
Truth Table and Logic Circuit from a Logical Function
Introduction to the Logical Function
- The session focuses on deriving a truth table and logical circuit from the logical function A cdot overlineB + C .
- Three variables are identified: A, B, and C. It is noted that these variables can repeat in combinations.
Combinations of Variables
- The number of combinations for three variables is calculated using 2^n , where n = 3 . This results in 8 combinations (from 0 to 7).
- Each combination must be converted into binary format, represented as three bits corresponding to A, B, and C.
Binary Representation
- The binary representations for numbers 0 through 7 are outlined:
- 0:
000
- 1:
001
- 2:
010
- 3:
011
- 4:
100
- 5:
101
- 6:
110
- 7:
111
Evaluating the Output
- To determine outputs for each combination, the logical function needs evaluation. Starting with combination zero (
000):
- For inputs A = 0, B = 0, C = 0; output is calculated as follows.
- For input combination one (
001), after substituting values into the formula:
- Output changes from low (0) to high (1).
Continuing Evaluation of Combinations
- Combination two (
010) yields an output of zero due to all inputs being zeros.
- Combination three (
011) also results in an output of zero based on similar logic.
Further Combinations Analysis
- In combination four (
100), since A is high while B and C are low, it leads to an output of zero.
- For combination five (
101), the output evaluates to one due to active inputs.
Final Outputs and Circuit Construction
- Combination six's outcome is determined by previous evaluations leading back to zero.
- Finally, for combination seven (
111), all inputs being high results in an output of one.
Constructing the Logic Circuit
- The construction involves drawing connections based on evaluated outputs.
- An OR gate combines inputs A and negated B.
- The final circuit design includes necessary NOT gates for negation before summing through OR gates.