UPC EETAC Bachelor's Degree in Telecommunications Systems and in Network Engineering EEL

Chapter 1 problems

      - A1.3 -

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.

Symbol and truth table

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