7.14 Problems

Chapter 7.14 Problems

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • CHAPTER 7. DIGITAL CIRCUITS1567.14Problems1. Using only two-input NOR gates, show how AND, OR and NAND gates can be made.2. The binary addition of two 2-bit numbers (with carry bits) looks like the following:C2C1X1X0+Y1Y0Z2Z1Z0(a) Write a truth table expressing the outputs C2 and Z1 as a function of C1, X1 andY1.(b) Write an algebraic statement in Boolean algebra describing this truth table.(c) Implement this statement using standard (AND, OR, EX-OR and inverter gates).3. If the 3-bit binary number ABC represents the digits 0 to 7:(a) Make a truth table for A, B, C and Q, where Q is true only when an odd numberof bits are true in the number.(b) Write a statement in Boolean algebra for Q.(c) Convert this equation to one that can be mechanized using only two XOR gates.Draw the resulting circuit.4. You need to provide a logic signal to control an experiment. The experiment is con-trolled by the four signals A, B, C and D, which make up the data word ABCD.Thecontrol line Q should be set high only if this data word takes on the values 1, 3, 5, 7,11 or 13.(a) Write a truth table for this function.(b) Using boolean algebra, write an expression indicating when Q is true.Yourstatement should include one logical statement for each of the six true conditions,each separated by the OR function. Therefore this statement should utilize anumber of AND/NAND functions, and five OR statements.(c) Simplify this statement so that it can be implemented using two two-input ANDgates, one OR gate, one exclusive OR gate and one logical inverter. The expressionhas the form Q =( )·{( )+( )· [( )⊕ ( )]}, where ( ) stands for any of the fourinput signals or their logical inverses.(d) Implement this simplified function using logic gates.