Combinational versus Sequential Circuits

1.23 (Combinational versus Sequential Circuits) Which of the fol¬lowing contain circuits that are likely to be combinational and which contain sequential circuits? Explain your rationale. (a) A washing machine that sequences through the soak, wash, and spin cycles for preset periods of time. (b) A circuit that divides two 2-bit numbers to yield a quotient and a remainder. (c) A machine that takes a dollar bill and gives three quarters, two dimes, and a nickel in change, one at a time through a single coin change slot. (d) A digital alarm clock that generates an alarm when a preset time has been reached. (e) A circuit that takes as input two decimal numbers in the range... click for more

Regular Logic Implementations

4.21 (Regular Logic Implementations Methods)Given the functions X, Y, and Z, defined by: X(A,B,C,D) = Σ m(1,2,3,5,7,9,11,13,15) Y(A,B,C,D) = Π Μ(2,3,4,5,6,7,8,10,12,14) Z(A,B,C,D )= Σ m(0.1.2.3.5.7) (a) Find the minimum sum of products form for each of these functions. How many unique product terms are there in your answer? (b) Find an alternative sum of products sum for X, Y, and Z that minimizes the number of unique product terms to implement all three functions simultaneously. How many unique product terms do you find in this implementation? (c) Show how to implement your solution to part (b) in a PLA structure.

Logic Implementation Methods

4.25 (Regular Logic Implementation Methods) You are to implement a combinational multiplier. It has two 2-bit inputs and a 4-bit output. The first 2-bit input is represented by the variables A, B; the second 2-bit input is represented by C, D. The outputs are W X, Y, Z, from the most-significant bit to the least. (a) Complete a truth table that describes the functional behav¬ior of the multiplier. (b) Find the minimum sum of products forms for the outputs using the K-map method. (c) Implement the multiplier using the P16H8 PAL of Figure 4.42. How many of these PALs do you need.

Logic Implementation

4.21 (Regular Logic Implementations Methods)Given the functions X, Y, and Z, defined by: X(A,B,C,D) = Σ m(1,2,3,5,7,9,11,13,15) Y(A,B,C,D) = Π Μ(2,3,4,5,6,7,8,10,12,14) Z(A,B,C,D )= Σ m(0.1.2.3.5.7) (a) Find the minimum sum of products form for each of these functions. How many unique product terms are there in your answer? (b) Find an alternative sum of products sum for X, Y, and Z that minimizes the number of unique product terms to implement all three functions simultaneously. How many unique product terms do you find in this implementation? (c) Show how to implement your solution to part (b) in a PLA structure

Digital Encoding

(Encoding) To digitally manipulate information we must encode it using binary numbers. Consider an encoding for playing cards. There are 52 cards in a deck and they are divided into four suits with values from 1 to 13 (an Ace is 1, Jack is 11, Queen is 12, King is 13). Show two possible encodings for the cards.