$(20$ points$)$ Design a $16-$bit binary parallel adder using TTL $74283$ chips. Show the schematic diagram.

$(20$ points$)$ Design a $8-$bit binary subtractor using TTL $74$x$283$ chips. Show the schematic diagram.

$(30$ points$)$ For the following circuit, determine the sum outputs for the following cases $($show your works$).$

$($a$)A=1101,B=0101,$ADD$=1,$SUB$=0$

$($b$)A=1101,B=0101,$ADD$=0,$SUB$=1$

$($c$)A=1101,B=0101,$ADD$=0,$SUB$=0$

$(30$ points$)$ Determine $F,C_{N+1},$ and OVR outputs for the following inputs to $74$LS$382($show your works$).$

$($a$)[S]=011,[A]=1100,[B]=0110,C_N=0$

$($b$)[S]=100,[A]=1100,[B]=0110,C_N=0$

$($c$)[S]=010,[A]=1100,[B]=0110,C_N=1$

Notes: S inputs select operation. OVR $=1$ for signed$-$number overflow.

$B=4-$bit input number

$B=4-$bit input number $C_{N+4}=$ carry out $ofMSB$ position

$C_N=$ carry into $LSB$ position OVR $=$ overflow indicator

$S=3-$bit operation select inputs