Boolean Algebra and Digital Circuits
Answer: (ABCD)' = A' + B' + C' +D'
Verification using Truth Tables:
LHS:
RHS:
From the above two tables it is clear that the values of LHS=RHS.
That means (ABCD)' = A' + B' + C' + D'
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Boolean Algebra and Digital Circuits 3. [5 pts total] Complete the following expression to state DeMorgan's...
PROBLEMS 1-1. Determine by means of a truth table the validity of DeMorgan's theorem for three variables: (ABC)' = A' + B' + C'. Simplify the following expressions using Boolean algebra. a. A +AB b. AB + AB c. A'BC + AC d. A 'B +ABC" + ABC 1-3.
Boolean algebra serves to relate logical quantities. The Boolean expression for the OR operation is C = A + B. Look up and write the Boolean expression for the AND operation. Write the truth table of the three-input operation D = A + (BC). Using truth tables, show that NOT(A + B) = (NOT(A))(NOT(B)) and similarly that NOT(AB) = ?
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
Using DeMorgan's law determine which of the following Boolean expressions are equivalent to the Boolean expression shown below. Y =(A+B)D+C AY = (ABDC) BY = (A+B)(D+) CY - (AB+DC D. Y = (AB)+(DC) EY = A +B) + (D+C) F. Y = (AB+D) +
please show full work and #rules needed 5. (5 pts) Using the DeMorgan's Theorem to implement the Boolean expression F = (AB)+(CD)' only with two-input NAND gates.
4. Using the bubble method (visual DeMorgan's Theorem) to draw circuits that will implement the following Boolean expression using only universal gates A & B & C) (C & ~B) | (A & B& C) (A B C) | (C & (A &B & C))
4. Using the bubble method (visual DeMorgan's Theorem) to draw circuits that will implement the following Boolean expression using only universal gates. (A & B& C)C&-B)l(A & B & C) -(-A I-BÍC) | (C & ~(A & B & C))
5. Apply Boolean algebra theorems to minimize the following expression. x(y + xy) + xy(x + yy) 6. Consider the following digital circuit diagram. Write the corresponding logic expression for f and the truth table. D A $(91, 02, ) f(x1, X2, X3)
Question 3: For the logic circuit given below: A (3 pts) Write Boolean expression for output X. a. B b. (5 pts) Simplify above expression using Boolean Algebra (2 pts) Draw the digital circuit based on the simplified expression. C.
Prove that: A'+B'+C'+D' = A'B'C'D' using theorems of boolean algebra to prove DeMorgans theorem for four variables