Description
Problem 1. The operation of a 4-to-1 multiplexer is described in the function table below:
s1 s0 Mux output
0 0 x0
0 1 x1
1 0 x2
1 1 x3
The symbols {x3, x2, x1, x0} represent the input “data” signals to the device, and symbols {s1, s0}
represent “select” signals that determine which one of the input signals will appear at the output. By
convention, the binary pattern associated with the select signals will match the subscript of xi. (For
example, if {s1, s0} = 10, then x2 is passed to the output.)
a) Write a Boolean logic equation that represents a 4-to-1 multiplexer. Use symbol F to represent the
output.
b) Draw a logic diagram (using logic gates, not simply a multiplexer symbol) that matches your
answer in part (a). (Neatness counts!)
Problem 2.
a) Create a function table for a 2-to-1 multiplexer. Follow the naming conventions given in the
previous problem.
b) Draw a logic diagram (using logic gates, not simply a multiplexer symbol) that matches your
answer in part (a).
Problem 3. The following logic diagram contains one standard logic gate (an inverter) and two 3-state
gates (sometimes called tri-state gates). Each 3-state gate is indicated by the symbol “3.s.” near its
output, and each is enabled by an active-low signal shown at the side of the gate.
a) Write a Boolean equation that describes the output F of this logic diagram, as a function of the
signals A, B, and E.
b) In what sense is the diagram shown above related to the concept of a multiplexer? Provide a brief
description.
Problem 4. For this problem, assume that you are developing code in the C language for a 32-bit
CPU such as the PIC32. As usual, bit position 0 refers to the least-significant bit. Write a C function
that satisfies the description given in the header below. (Do not submit a separate source file for this
problem; just place your code as text into the file containing your HW solutions. You are not required
to compile and run your code, although that is recommended as a way for you to check your
solution.)
//////////////////////////////////////////
// Function name: getBitValue
// Input parameters:
// val: an arbitrary integer
// k: an integer, assumed to be in the range [0, 31]
// Returns:
// 1 if val contains a 1 at bit position k; else return 0
//
int getBitValue ( int val, int k )
{
}
Problem 5. The flip-flops in the following diagram are positive-edge-triggered devices. Complete the
timing diagram that is shown below. Assume that both flip-flops have been initialized to 0.
CLK
A
B
Q0
Q1
F
