VBE$($FA$)=0\mathrm{.}7$V$,$ VBE$($SAT$)=0\mathrm{.}8$V$,$ VCE$($SAT$)=0\mathrm{.}2$V$,$ VBC$($RA$)=0\mathrm{.}7$V$,$ VDIODE$($ON$)=0\mathrm{.}7$V F$=100,$ R$=0\mathrm{.}1.$ Vcc $=5$V

a$)$ For the TTL inverter given in Figure $2,$ using given electrical specifications, find the operation mode of each BJT$.$ Calculate IB$4,$ IC$4,$ IB$5,$ IC$5$ when VIN$=0$V and VIN$=5$V respectively.

b$)$ Sketch the voltage transfer characteristics by finding VOL, VOH, VIL, VIH.

c$)$ Calculate the high and low noise margins.