A function given by a logical expression write in the truth table.

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SUMMARY

The discussion centers on constructing a truth table for the logical expression Y = A.B.D + A.not(C).D + A.not(B).C.D + A.D. The truth table evaluates all combinations of the variables A, B, C, and D, resulting in the output Y. The analysis concludes that the function Y will yield a value of 1 only when both A and D are 1, irrespective of the values of B and C. This simplifies the expression to Y = A.D.

PREREQUISITES
  • Understanding of logical expressions and Boolean algebra
  • Familiarity with truth tables and their construction
  • Knowledge of logical operators such as AND, OR, and NOT
  • Basic skills in evaluating logical functions
NEXT STEPS
  • Study Boolean algebra simplification techniques
  • Learn about Karnaugh maps for minimizing logical expressions
  • Explore digital logic design principles
  • Investigate the implementation of logical functions in programming languages
USEFUL FOR

This discussion is beneficial for students in computer science, electrical engineering, and anyone involved in digital logic design or Boolean algebra analysis.

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Assignment:
A function given by a logical expression Y = A.B.D + A.not (C) .D + A.not (B) .C.D + A.D write in the truth table.
 
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A B C D Y0 0 0 0 00 0 0 1 00 0 1 0 00 0 1 1 00 1 0 0 00 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 01 0 0 1 01 0 1 0 01 0 1 1 11 1 0 0 01 1 0 1 11 1 1 0 01 1 1 1 1
 


| A | B | C | D | Y |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |

In this truth table, A, B, C, and D represent different logical variables, and Y represents the output of the function. The function is evaluated for every possible combination of inputs, and the corresponding output is shown in the last column. Based on the given logical expression, the output Y will be 1 only when A is 1 and D is 1, regardless of the values of B and C. Therefore, the truth table shows that the function Y = A.D.
 

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