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Again with a question about truth tables! Here there's an error somewhere... can you help me?

This is my truth table:

    CD | 00 | 01 | 11 | 10
 AB    |    |    |    |
 ------+----+----+----+----
 00    |  1 |  1 |  0 |  0
 ------+----+----+----+----
 01    |  0 |  1 |  1 |  0
 ------+----+----+----+----
 11    |  1 |  1 |  0 |  0
 ------+----+----+----+----
 10    |  1 |  1 |  0 |  0
 ------+----+----+----+----

This should be the correct result:

f=B'C'+C'D+A'BD+AC'

And these are my (wrong?) results:

f=A'B'C'D'+A'B'C'D+A'BC'D+A'BCD+ABC'D'+ABC'D+AB'C'D'+AB'C'D

f=A'B'C'(D'+D)+A'BD(C'+C)+AC'(BD'+BD+B'D'+B'D)

f=A'B'C'+A'BD+AC'

Can you help me? Thanks a lot in advance!

Cholesky
  • 15

1 Answers1

1

You did not make a mistake, you just haven't simplified it far enough. In your last expression,

$$f=A'B'C'+A'BD+AC'$$

take the first and last terms and factor out $C'$. We then use the redundancy law $X+X'Y=X+Y$ to simplify.

$$f=C'(A'B'+A)+A'BD=C'(B'+A)+A'BD=B'C'+A'BD+AC'$$

Riley
  • 2,747