A traffic light control at Kafue round about uses, a binary counter to produce the following sequence of combinations on lines A$.$ B$.$ C$.$ and D$.0000.0001.0011.0010.0110.0111.0101.0100.1100.1101.1111.1110,1010.1011,1001.1000.$ After $1000,$ the sequence repeats, beginning again with $0000,$ forever. Each combination is present for $5$ seconds before the next one appears. These lines, drive combinational logic with outputs to lamps RNS $($Red$.$ North$/$South$).$ YNS $($Yellow $-$ North$/$South$).$ GNS $($Green$$ North$/$South$).$ REW $($Red$$ East$/$West$).$ YEW $($Yellow$-$ East$/$West$).$ And GEW $($Green$-$East$/$West$).$ The lamp controlled by each output is ON for a $1$ applied and OFF for a $0$ applied. For a given direction, assume that green is on for $30$ seconds, yellow is on for $5$ seconds. And red is on for $45$ seconds. $($The fed intervals overlap for $5$ seconds.$)$ Divide the $80$ seconds seconds available for the cycle through the $16$ combinations into $16$ intervals and determine which lamps should be lit in each interval based on expected driver behavior. Assume that, for interval $0000,$ a change has just occurred and that GNS $=1.$ REW $=1.$ and all other outputs are $0.$ Design the logic to produce the six output using AND and OR gates and inverters