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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 the segments in the display indicator used for displaying the decimal digit in the familiar form. The seven output of the decoder(a,b,c,d.e.f) selects the corresponding segments in the display c as shown in figure (a). The numeric designation chosen to display the decimal digit is shown in Fig (b).

Design the BCD to Seven-segment decoder using the minimum number of the NAND gates.

the Six invalid combinations should result in a blank display.

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 Decimal A B C D a b c d e f g 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 2 0 0 1 0 1 1 0 1 1 0 1 3 0 0 1 1 1 1 1 1 0 0 1 4 0 1 0 0 0 1 1 0 0 1 1 5 0 1 0 1 1 0 1 1 0 1 1 6 0 1 1 0 1 0 1 1 1 1 1 7 0 1 1 1 1 1 1 0 0 0 0 8 1 0 0 0 1 1 1 1 1 1 1 9 1 0 0 1 1 1 1 1 0 1 1 10 1 0 1 0 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ 11 1 0 1 0 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ 12 1 1 0 0 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ 13 1 1 0 1 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ 14 1 1 1 0 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ 15 1 1 1 1 $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$ $\phi$

$\phi: \text{Don't care}$

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