Digital Systems

Q1. Design, implement and verify a digital circuit that indicates whether a 4-bit unsigned number is triangular or not (see Wikipedia). The steps are: (a) State the truth table for the circuit. (b) State the Boolean expression for a standard Sum Of Products implementation of the circuit. (c) Implement and verify the standard Sum Of Products circuit in Logisim. (d) Using Karnaugh maps, obtain a minimal Sum Of Products Boolean expression for the circuit. (e) Implement and verify the minimal Sum Of Products circuit in Logisim, (f) Determine the area of the two implementations in terms of Gate Equivalents. (g) Determine the delay of the two implementations in terms of Gate Equivalents. (h) What are the percentage area and delay savings of the smaller and faster circuits? Submit the circuits. Q2. Using Boolean logic gates, design, implement and verify a digital circuit that indicates whether a 4-bit unsigned number is a digit in your student number or not. For example, if your student number is 00123456, the circuit should output a TRUE value if the inputs is 0,1,2,3,4,5 or 6 and a FALSE otherwise. The steps are the same as in Q1. Submit the circuits.