I am trying to re-implement the BCD to 7-SEGMENT converter by hand. So, I have came up with the following truth table:
I have the following minimization created with the Karnaugh map. Is there any way to minimize this more?
2
-
\$\begingroup\$ Are you trying to minimize terms or gates? \$\endgroup\$– Ignacio Vazquez-AbramsCommented Jun 6, 2014 at 7:03
-
\$\begingroup\$ gates and terms if possible \$\endgroup\$– VictorCommented Jun 6, 2014 at 7:34
Add a comment
|
1 Answer
\$\begingroup\$
\$\endgroup\$
2
Invert it. Inverted logic often gives better results if there are more 1's than 0's.
When minimising gates also group similar subexpressions so they can share gates.
$$a = \overline{\overline{ABC}D + \overline{A}B\overline{CD} + A\overline{B}CD + AB\overline{C}D}\\ = \overline{\overline{AC}(\overline{B}D+B\overline{D}) + AD(\overline{B}C+B\overline{C})}\\ =[A+C+(B+\overline{D})(\overline{B}+D)][\overline{A}+\overline{D}+(B+\overline{C})(\overline{B}+C)]\\ =(A+C+\overline{BD}+BD)(\overline{A}+\overline{D}+\overline{BC}+BC)\\ =(A+C+\overline{B\oplus D})(\overline{A}+\overline{D}+\overline{B\oplus C})$$
-
\$\begingroup\$ but it doesn't work... below is a link to my circuit. the probe stays always on. imgur.com/mIW1kh7 \$\endgroup\$– VictorCommented Jun 6, 2014 at 17:23
-
\$\begingroup\$ Your circuit have several errors so it does not work. Upper XOR/OR is $A+\overline{C}+B\oplus D$ instead of $A+C+\overline{B\oplus D}$. \$\endgroup\$– VovaniumCommented Jun 9, 2014 at 11:34