﻿ Digital Circuits and Systems - Circuits i Sistemes Digitals (CSD) - EETAC - UPC
 Bachelor's Degree in Telecommunications Systems and in Network Engineering

### Logic equations (PoS, SoP, maxterms, minterms)

1. Specifications

Fig. 1 shows the block diagram and the truth table of an 8-to-3 encoder (Enc_8_3), a typical next section (P2) example of standard circuit. When several inputs are active high at the same time, a binary code is generated of the highest priority signal. The symbol "-" means a "don't care" value that is represented other times by "x". GS goes high when any input is assessed, thus it can be used both as a flag to indicate that a key is pressed and for disambiguation of the code "000".

a) Represent the output Y2 = f(X7 .. X0) using a product of sums (PoS).

b) Represent the output Y1 = f(X7 .. X0) using a sum of products (SoP).

c) Represent the output GS using maxterms. How many minterms will the function have?

d) Write down the single-file (flat) VHDL code using either structural (plan A) or behavioural (plan B) style. Explain the differences between the two coding styles.

 Fig. 1. The symbol and truth table of a combinational circuit.