E15: Fundamentals of Digital Systems - Fall 2015 - HOMEWORK 2
1. Convert these decimal numbers to binary using either of the methods we discussed in class. Show your work.
a. 53
b. 27
c. 119
2. Compute the decimal values of these binary numbers (you don't need to show your work).
a. 10010
b. 11111111
c. 1010
3. Simplify these functions using Karnaugh maps to form a sum of products:
a. F(w, x, y, z) = Σ(0, 1, 2, 8, 9, 10, 12, 13)
b. F(a, b, c, d) = Σ(0, 1, 2, 3, 4, 6, 8, 9)
4. Simplify these functions using Karnaugh maps to form a product of sums:
a. F(A, B, C, D) = Σ(3, 4, 5, 6, 7, 10, 11, 14, 15)
b. F(w, x, y, z) = Σ(0, 1, 2, 8, 9, 10, 12, 13)
5. Implement your answer to 3a. above in Verilog by instantiating primitives for each gate.
Hand in a printout of the module source, test bench source, and also a printout of the waveform traces, showing successful testing of all sixteen cases.
6. Implement your answer to 4a. above in Verilog by using continuous assignment statements and logic operators similar to HDL example.
Hand in a printout of the module source, test bench source, and also a printout of the waveform traces, showing successful testing of all sixteen cases.
7. Consider the digital seven-segment display (as found, for instance, on a digital alarm clock). Specifically, we will focus on the center segment - that is the one which is enabled for the number 8 but not the number 0. Let b3, b2, b1, b0 be the bits (from MSB to LSB) of a 4-bit binary number. The truth table mapping these bits to the center segment is given by
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b3
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b2
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b1
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b0
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F
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0
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0
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0
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0
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0
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0
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0
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0
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1
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0
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0
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0
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1
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0
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1
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0
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0
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1
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1
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1
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0
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1
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0
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0
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1
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0
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1
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0
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1
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1
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0
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1
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1
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0
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1
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0
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1
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1
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1
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0
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1
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0
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0
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0
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1
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1
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0
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0
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1
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1
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1
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0
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1
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0
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X
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1
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0
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1
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1
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X
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1
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1
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0
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0
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X
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1
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1
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0
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1
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X
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1
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1
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1
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0
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X
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1
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1
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1
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1
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X
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a. Why are minterms 10 through 15 marked as don't care?
b. Use a Karnaugh map to form a sum of products for F, taking advantage of the don't care terms.
c. Use a Karnaugh map to form a product of sums for F, taking advantage of the don't care terms.