ECE 265 Experiment 2: Design of a Programmable Digital Logic Gate In this laboratory experiment your task is to design a combinational digital logic circuit having 4 inputs and one output, whose purpose is to implement one of four different logic functions depending on which one is selected. Two of the circuit’s inputs are a and b, the other two inputs are s1 and s0, and the output is x = f{s1s0, a, b}: Here is how this programmable digital logic gate should operate: • When select inputs s1s0 = 00, then x = a AND b • When select inputs s1s0 = 01, then x = a OR b • When select inputs s1s0 = 10, then x = a XOR b • When select inputs s1s0 = 11, then x = a XNOR b ECE 265 Experiment 2 (page 1 of 3) Both partners: 1. Draw a truth table for output variable x in terms of input variables {s1s0, a, b}. Partner A: 2. Write an expression for x = f{s1s0, a, b} as a sum of minterms. 3. Simplify the sum-of-minterms expression in (2) to reduce the number of literals as much as you can. Show every step, and state what Boolean algebraic property was used for each simplification. 4. Use CircuitVerse to build a circuit that implements the simplified expression from (3), using only 2-input {AND, OR} gates and inverters. 5. Convert the circuit from (4) to one having only 2-input NAND gates. Simulate this circuit in CircuitVerse to verify that it correctly implements the specified logic function. Label each circuit with its cost according to the formula: cost = $0.10 per {gate or inverter}. Partner B: 6. Write an expression for x = f{s1s0, a, b} as a product of Maxterms. 7. Simplify the product-of-Maxterms expression in (6) to reduce the number of literals as much as you can. Show every step, and state what Boolean algebraic property was used for each simplification. 8. Use CircuitVerse to build a circuit that implements the simplified expression from (7), using only 2-input {AND, OR} gates and inverters. 9. Convert the circuit from (8) to one having only 2-input NOR gates. Simulate this circuit in CircuitVerse to verify that it correctly implements the specified logic function. Label each circuit with its cost according to the formula: cost = $0.10 per {gate or inverter}. Both partners: 10. Use CircuitVerse to realize x = f{s1s0, a, b} using one 4 × 1 multiplexer and any number of 2-input logic gates. Label this circuit with its cost according to the formula: cost = $1.30 (4×1 mux) + $0.10/gate. ECE 265 Experiment 2 (page 2 of 3) Work together with your assigned partner. Discuss the problems and their solution approaches. Divide up the work load, understand and check each other’s work. You will then each submit a lab report, including work asked for above, and links to the simulated circuits saved "public" in CircuitVerse. For example: Partner "A" submits his/her work plus the work done by Partner "B", but rewritten so that the combined result flows nicely as if one person wrote it. Each partner should do this in their own hand – duplicate submissions will not count. In case your partner cannot be contacted or does not contribute, then do all of the work yourself (and later assess the partner’s contribution as 0%). When a pattern develops, non-contributors will be penalized. Ideally, each partner should contribute 50% to the group effort. Remember: being able to work well with others takes practice and is a vital engineering skill! ECE 265 Experiment 2 (page 3 of 3)