$(9)$

Combinational Logic Design

Consider the seven$-$segment display for hexadecimal computation as shown in Fig. P$-9$A$.$ The hexadecimal number wxyz is used to represent $\backslash (0,1,2,3,4,5,6,7,8,9,\backslash$mathrm$\{$~A$\},\backslash$mathrm$\{$~B$\},\backslash$mathrm$\{$C$\},\backslash$mathrm$\{$D$\},\backslash$mathrm$\{$E$\}\backslash ),$ and F $.$

$(9$a$)$ Fill in the truth table for the strokes a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ and g$.$ You may use the table Fig. P$-9$B below.

Fig. P$-9$B

$7$ marks

$(9$c$)$ Use an $\backslash (8\backslash$times $4\backslash )$ ROM to realize the strokes $"$ f $"$ and $"$ g $",$

You may use the figure Fig. P$-9$D as provided below.

$(9$b$)$ Realize the stroke $"$c$"$ using two $4$:$1$ MUXes and one $2$:$1$ MUX. You may use the figure Fig. P$-9$C provided below.

$(9$c$)$ Use an $\backslash (8\backslash$times $4\backslash )$ ROM to realize the strokes $"$ f $"$ and $"$ g $".$

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