EECS 151/251A Homework 1
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1 EECS 151/251A Homework 1 Due Friday, January 26 th, 2018 roblem 1: Computing Systems A wide range of computing systems are currently in production. Consider the following devices when answering the questions below: a laptop, a digital watch, a scientific calculator, a supercomputer, and a smartphone. (a) Sketch a curve showing computational performance of all these systems as a function of their cost. ut performance on the y-axis (arbitrary units), and cost on the x-axis (dollar estimate). (b) Similarly, show a curve that relates computational performance to system power con- sumption, with performance on the y-axis (arbitrary units), and power consumption on the x-axis (watt estimate). In the case of the smartphone, ignore the power consumption of the radio. (a) erformance (IS)! 1.E+16! 1.E+14! Supercomputer! 1.E+12! 1.E+10! 1.E+08! Smartphone! Laptop! 1.E+06! 1.E+04! (b) 1.E+02! Scientific Calculator! Digital Watch! 1.E+00! 1.E+00! 1.E+01! 1.E+02! 1.E+03! 1.E+04! 1.E+05! 1.E+06! 1.E+07! 1.E+08! 1.E+09! Cost ($)! erformance (IS)! 1.E+16! 1.E+14! Supercomputer! 1.E+12! 1.E+10! 1.E+08! Smartphone! Laptop! 1.E+06! 1.E+04! 1.E+02! Digital Watch! Scientific Calculator! 1.E+00! 1.E-08! 1.E-06! 1.E-04! 1.E-02! 1.E+00! 1.E+02! 1.E+04! 1.E+06! ower Consumption (W)!
2 EECS 151/251A Homework 1 2 roblem 2: Logic Consider the circuit below. All inputs (,, D 0, D 1, D 2, and D 3 ) must be tied to 0 or 1. D 0 D 1 F D 2 D 3 (It might help to simplify this circuit, as you would with the kind of powerful diagramming tool I do not have.) (a) What must D 0, D 1, D 2, D 3 be such that F =? (b) Can any arbitrary 2 input logic function of signals and be realized using the above architecture? Explain. (a) D 0 = D 3 = 0 D 1 = D 2 = 1 (b) Yes, the circuit is essentially equivalent to a 4-input MUX, where one of D 0, D 1, D 2, and D 3 is selected based on the values of the and inputs. Each possible state of and will select one of D 0 through D 3, and so by choosing the D 0 through D 3 values, we can implement any desired single-output truth table (logic function) of the and inputs. roblem 3: Logical Gates You work for Sldgly, a start-up in San Francisco that uses the sludge found in the Bart transit system to perform logic functions. They call this device a Sludge Gate; every Sludge Gate requires a supply and ground, has input signals X and Y, and produces an output signal Z.
3 EECS 151/251A Homework 1 3 Here is the behavior of the Sludge Gate with a 5 V supply: 0 < Z < 5V If X and Y have less than 2 V at the input for 5 microseconds or more, then Z is greater than 4 V When either or both of X and Y have more than 3.5 V for at least 5 microseconds, then Z is less than 1 V The exact voltage at Z is unpredictable and varies from Sludge Gate to Sludge Gate. (a) ropose a simple topology using Sludge Gates to invert an input signal, S. (b) For the inverter in (a) draw a very simple voltage transfer curve, making sure to label key voltages on both axes. (c) What Boolean function of X and Y does the Sludge Gate implement? (a) Either of: (b)
4 EECS 151/251A Homework 1 4 (c) NOR gate: Z = (X + Y )
5 EECS 151/251A Homework 1 5 roblem 4: Structural Verilog Write modules using structural Verilog which implement the circuit drawn below. You will need multiple module statements to preserve the hierarchy as drawn. a majority3 b m c top x[0] x[1] x[2] a b c majority3 m y[0] y[1] y[2] a b c majority3 m out
6 EECS 151/251A Homework 1 6 Solution: module majority3( input a, input b, input c, output m ); wire and0_out, and1_out, and2_out; // verilog primatives have no explicit port connection, // and the output is first and (and0_out, a, c); and (and1_out, b, a); and (and2_out, c, b); or (m, and0_out, and1_out, and2_out); endmodule module top( input [2:0] x, input [2:0] y, output out ); wire maj0_out, maj1_out; // instantiate the modules- note the explicit port connection majority3 maj0 (.a(x[0]),.b(x[1]),.c(x[2]),.m(maj0_out)); majority3 maj1 (.a(y[0]),.b(y[1]),.c(y[2]),.m(maj1_out)); and (out, maj0_out, maj1_out); endmodule roblem 5: Behavioral Verilog For the logic circuit shown below, write the equivalent behavioral Verilog module which takes A and B as inputs, and gives X as output.
7 EECS 151/251A Homework 1 7 Solution: module problem5( input A, input B, output X ); assign X = ~(~(~(A ~B) (A & B)) & (A B)); endmodule Note: You still receive full credit if wrote the HDL code for the simplified logic expression: X = ((A + B) + A B) (A + B) = X = A B + A B + A B Or they simplified the expression complete: A.B + A.B + A.B = A.B + A.B + A.B + A.B = A(B + B) + B(A + A) = A(1) + B(1) = A + B
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