A BCD$-$to$-$seven$-$segment decoder is a combinational circuit that converts a decimal digit in BCD to an

appropriate code for the selection of segments in an indicator used to display the decimal digit in a

familiar form. The seven outputs of the decoder $($a$,$ b$,$ c$,$ d$,$e$,$ f$,$ g$)$ select the corresponding segments in

the display, as shown in Figure $3($a$).$ The numeric display chosen to represent the decimal digit is shown

in Figure $3($b$).$

Using Karnaugh maps, design the BCD$-$to$-$seven$-$segment decoder using a minimum number of gates.

The six invalid combinations should result in a blank display.