$\backslash$table$[[2,3,4,5,6]]$

Check

Create the truth table for the seven$-$segment decoder and derive the optimized

Boolean expression in sum$-$of$-$products form.

Use a Karnaugh map $($K$-$map$)$ to minimize the equation for each output based on the

following segments:

$1$st: A$,$ F$,$ B$,$ E$,$ D$,$ C ON

$2$nd: B$,$ C ON

$3$rd: A$,$ B$,$ G$,$ E$,$ D ON

$4$th: A$,$ B$,$ G$,$ C$,$ D ON

$5$th: F$,$ G$,$ B$,$ C ON

$6$th: A$,$ F$,$ G$,$ C$,$ D ON

$7$th: A$,$ F$,$ G$,$ E$,$ D$,$ C ON

$8$th: A$,$ B$,$ C ON

$9$th: A$,$ B$,$ G$,$ F$,$ E$,$ D$,$ C ON

$10$th: A$,$ B$,$ G$,$ F$,$ C$,$ D ON

Complete the truth table, then write a logic equation for each output. Use K$-$maps or Boolean

algebra to find the minimized expressions.

In sum$-$of$-$products format, include only terms for outputs that are $1.$ Group cells with logic $1$ in

K$-$maps to form equations.

Note:

For decimal values $10$ to $15,$ set all segments to $1($indicating NOT lit$).$

Inputs: numin $[3],$ numin$[2],$ numin$[1],$ numin$[0]($use n$3,$ n$2,$ n$1,$ n$0$ for manual

work$).$

Outputs: segout $[6]$ to segout $[0]$ instead of A to G$.$

$\backslash$table$[[\backslash$table$[[$numin$],[3$

Create the truth table for the seven$-$segment decoder and derive the optimized

Boolean expression in sum$-$of$-$products form.

Use a Karnaugh map $($K$-$map$)$ to minimize the equation for each output based on the

following segments:

$1$st: A$,$ F$,$ B$,$ E$,$ D$,$ C ON

$2$nd: B$,$ C ON

$3$rd: A$,$ B$,$ G$,$ E$,$ D ON

$4$th: A$,$ B$,$ G$,$ C$,$ D ON

$5$th: F$,$ G$,$ B$,$ C ON

$6$th: A$,$ F$,$ G$,$ C$,$ D ON

$7$th: A$,$ F$,$ G$,$ E$,$ D$,$ C ON

$8$th: A$,$ B$,$ C ON

$9$th: A$,$ B$,$ G$,$ F$,$ E$,$ D$,$ C ON

$10$th: A$,$ B$,$ G$,$ F$,$ C$,$ D ON

Complete the truth table, then write a logic equation for each output. Use K$-$maps or Boolean

algebra to find the minimized expressions.

In sum$-$of$-$products format, include only terms for outputs that are $1.$ Group cells with logic $1$ in

K$-$maps to form equations.

Note:

For decimal values $10$ to $15,$ set all segments to $1($indicating NOT lit$).$

Inputs: numin$[3],$ numin $[2],$ numin$[1],$ numin$[0]($use n$3,$ n$2,$ n$1,$ n$0$ for manual

work$).$

Outputs: segout $[6]$ to segout $[0]$ instead of A to G$.$