4. (8 Points) Using a truth table, prove the following statements are logically equivalent. Be sure to include an explanation of how your truth table demonstrates this conclusion. -(X VY)= -X A-Y
Prove or disprove the following expression. (Prove: using Boolean algebra. Disprove: using truth table.) (NOT is presented by -.) 1. a + b (c^- + d)^- = a^-b^- + a^-cd^- 2. ab^- + bc^- + ac^- = (a + b + c) (a^- + b^-+ c^-) 3. a^- + bd^-^- (c + d) + ab^-d = ac^-d + ab^-cd + abd
Prove or disprove (without using a truth table): (p^q) rightarrow (q rightarrow p) is a tautology. Prove that the contrapositive holds (without using a truth table), that is that the followi holds: p rightarrow q identicalto q rightarrow p
Prove the following is a tautology (without using a truth table) [(p →q) (q + r)] → (p → r)
Home work AB tAC t ABC A+BC Prove by truth table (AB)(A+B)C = A BC A+B ABC 2 Prove hy tra teble AAB+BAB + BA AB RB) ABc
[4] (a) For the given expression draw the TRUTH TABLE Y = A B C+A.BC (b) From the truth table derive the POS EXPRESSION and implement it by basic gates (c) Redraw the logic diagram by using only universal gates. [1+1+2=4]
2. Prove that A+B AB by: a. b. c. d. Using truth tables for both the right and right sides of the equation. Drawing a gate level schematic for both the right and right sides of the equation Which theorem is this? Restate the theorem in terms of gates.
Need to prove if this letter statement is a tautology using the tautology test 2. Prove or disprove using the Tautology Test that ((An, B'),-(BAA')) → (AVB) is a tautology. ABCD
Q3 (30 pts): Use the truth table to prove the validity of the expression: Overflow Cn-1 for addition of n-bit signed numbers. Hint: construct first the truth table for both Overflow and cn, as a function of xn-1yn-1. and
Fill the truth table . 4-4) Fill in the truth table below, build your circuit and test it for those six cases. Adder-Subtractor Truth Table Input Expected Output Circuit Output A4, A3, A2, A1 Sign of B B4, B3, B2, B1 | 04 | 54 | 53 | 52 | si Same as expected? Note any discrepancies. 1001 0101 1001 0101 1001 1001 1001 1001 1001 1 + 1111 1001 1111