(Solved):   A digital dice can throw a binary number in the range 1 to 6 . Use two digital die to buil ...

 

A digital dice can throw a binary number in the range 1 to 6 . Use two digital die to build a combinational system that shows an output, named \( B \), that indicates when the first dice is throwing either a 1 or a 5 while the second dice is throwing either a 2 or a 6 . Note that the conditions for each dice must met simultaneously to appropriately display output B. (a) Construct suitable truth tables to model the solution as a combinational system each dice independently. Clearly indicate the names of your variables including required outputs and briefly explain the truth tables. (6 marks) i) Obtain logic equations for the output of each dice in the form of sum-ofproducts of minterms. (5 marks) ii) Use either Boolean algebra or Karnaugh maps to minimise the two logic equations representing each dice. (5 marks) (b) Construct a suitable truth table to model the whole combinational system composed of the two die together. Clearly indicate the names of all required variables and provide a sum-of-products of minterms equation for the output \( B \). (4 marks) (c) Draw a logic circuit for the minimised combinational system generating output B using any of the standard logic gates. Label all inputs and outputs appropriately. (5 marks)