Convert the binary numbers $02(0$:$0)$ through $1010,(1010)$ into ternary. This becomes very complex with our current methods at scale, so we are only interested in finding the first ternary bit, or least significant bit $($LSB$).$ Looking at the table below... H Hex $0120$ DCBA XYZ X Y Dec Bin Tern Bin Bin $00000000000000100011000000002001020000000030011100000000140100110000000150101120000000160110200000001070111210000001081000220000001010011000001000010101010100010000$ Z Bin $00000001001000000001001000000001001000000001000201201...$you will notice that we can have four binary bits $($Z$3,$ Z$2,$ Z$3,$ Zo$)$ representing the ternary bit $"$Z$".$ The hex value on the far right is derived from the binary representation of this bit. In LogicWorks, you would get this value using the Hex Display, as seen in labi and the diagram below, which is for an input of $1110.$ You must first derive the equations for each binary bit in z $($that is$,$ Z$3$ though Zo$),$ and then build the circuit that computes each one. Use only AND$-2$ and OR$-2$ gates. For input, it is suggested that you use a Hex Keyboard instead of binary switches for DCBA inputs. $2322212001$ D C B A Z Out $1011$ Input $(11)0123$ Conversion $89$ AB logic $00$ N $24567$ CDEF