HW #3 Solutions (Preliminary - does not include warmup problems) CSEE W3827 - Fundamentals of Computer Systems

HW #3 Solutions (Preliminary - does not include warmup problems) CSEE W3827 - Fundamentals of Computer Systems Fall 2018 Prof. Rubenstein Topics: Standard circuitry (encoder, decoder mux), combinatorial circuit design Note that this homework has 5 problems and is 2 pages long. 1. (15 pts) Construct a 4-to-16 line decoder with an enable input using five 2-to-4 line decoders with enable inputs (Hint: Start at the outputs: If all that is being used is decoders, then how many decoders are connected directly to outputs?) 1 2. (10 pts) A combinatorial circuit is specified by the following three Boolean functions: F = X + Y¯ + XY Z ¯ Design the circuit with a decoder and external OR gates. F = X + Y¯ + XY Z ¯ = (XY¯Z¯ + XY Z¯ + XY Z¯ + XY Z) + (X¯Y¯Z¯ + X¯Y Z¯ + XY¯Z¯ + XY Z¯ ) + (XY Z ¯ ) = X¯Y¯Z¯ + X¯Y Z¯ + XY Z ¯ + XY¯Z¯ + XY Z¯ + XY Z¯ + XY Z = m0 + m1 + m3 + m4 + m5 + m6 + m7 2 3. (25 pts) A traffic light controller receives a 4-bit input that changes every 5 seconds. The input sequence is a simple counter that counts from binary 0 to binary 15 and then starts again from binary 0. These signals go to 4 outputs, NSH, NSL, EWH, EWL. The first two outputs NSH and NSL respectively represent the high and low bits that are fed to the lamps that face in the North-south direction. The other two outputs EWH and EWL respectively represent the high and low bits that are fed to the lamps that face in the East-West direction. The following table indicates how setting the high and low bits determines the color of th