Consider the characteristic polynomial: f(x) = 1 + x3 + x4 1.1. First, consider a standard (external) LFSR.

 Consider the characteristic polynomial: f(x) = 1 + x3 + x4 1.1. First, consider a standard (external) LFSR.  Draw the circuit, write the matrix equation, and show an example pattern sequence for this LFSR. 1.2. Second, consider a modular (internal) LFSR.  Draw the circuit, write the matrix equation, and show an example pattern sequence for this LFSR.
 2. Draw a transistor-level diagram of a three-input NAND gate and: 2.1. First, give an example input sequence required to detect a stuck-open fault in one of the NAND gate’s PMOS transistors 2.2. Second, give an example input sequence required to detect a stuck-open fault in one of the NAND gate’s NMOS transistors
 3. Count the number of fault sites present in the circuit shown to the right: Y = f(A,B,C,D).  In addition, how many primary inputs and primary outputs are present in this circuit?
 4. This problem is similar to homework 2.  Consider the example pipelined ripple-carry adder (RCA) shown to the right.  If this is a 4-bit RCA, what sequence of signals is required to set the sum to “0110” when A = “0100” and B = “1111”?  Use a scan-chain diagram similar to Figure 2.14 of the textbook and identify the pseudo-primary inputs (PPIs) and pseudo-primary outputs (PPOs).
 5. Explain the operations required to perform the INTEST JTAG (boundary scan) instruction.  To assist your explanation, please draw and use a figure to explain the required operations



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