B) (В Using the K-Map, find the logical expression. (A A C FLAB.C=ABC+ABC ABC)-A BC ABC FAB.CA BC+ABC TABCA8-ABC 1.

(1 point) Consider the points which satisfy the equation 3 y² = x² + ax + b mod p where a = 5, 61, and p = 7. Enter a comma separated list of points (x, y) consisting of all points in Z½-½ satisfying the equation. (Do not try to enter O, the point at infinity.) (0,1), (0.6),(1,0), (3,1), What is the cardinality of this elliptic curve group? 12

Let L = {aibkal | į>1+ k, and įj.k>=1} a) List all strings in L of length 8. b) Construct a state diagram PDA for L. (Do not create a table for the transition function)

7. Truc or Falsc. (a) For signed integer values, one obtains the most negative number by negating the most positive number. (b) In Verilog, if an if statement docs not have a corresponding else statement, a latch is inferred. (c) Minimization with a Karnaugh map produces a unique solution. (d) In Verilog, an if statement must always be inside of an always block. (c) FSM state minimization may lead to a less readable hardware description. (f) In Verilog, if we define input [1:-6] x; and input [0:-7] y;, then x+y adds a Q2.6 number and a Q1.7 number. (g) The direct form implementation of an FIR filter of order N requires N registers. (h) It is possible to build a NOT gate with a NOR gate. (i) An FSM with 25 states requires 5 flip-flops. (j) The sensitivity list for Moore and Mealy machines should contain only the input(s) and the clock.

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(d) Find Ce (e) Find A U BUC