$1.\backslash ((\backslash$mathbf$\{20\}\backslash$mathbf$\{$~ p t s$\})\backslash )$ LUT design $($LUT $\backslash (=\backslash )$

LookUp Table$)$

Design a digital logic circuit with three $($binary$)$ inputs: $\backslash (\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$z$\},(0-7\backslash )$ in decimal$)$ and the three $($binary$)$ outputs, A$,$ B$,$ and C$.$ When the binary input is $\backslash (0,1,2\backslash ),$ or $3,$ the binary output is $2$ greater than the input. When the binary input is $\backslash (4,5,6\backslash ),$ or $7,$ the binary output is $2$ less than the input.

Set$-$up the appropriate truth table, simplify using K$-$maps. Implement, using LogiSim, the simplified logic circuit with optimal number of logic gates.

$(20$ pts$)$ LEDs $($Light Emitting Diodes$)$

Three LEDs $($one Red, one Green, one Blue$)$ turn on when a decimal number $0-7[3($ x$,$y$,$z$)$

binary bits are required$]$ is passed through. Red turns on with even numbers, Green turns on

with odd numbers, Blue turns on with multiples of $3.$ Zero means they are all off, seven means

they are all on$.($all output numbers should be in binary$)$

Set$-$up the appropriate truth table, simplify using K$-$maps. Implement, using LogiSim,

the simplified logic circuit with optimal number of logic gates.