Columbia University

CSEE W3827

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