Q3: A) Express the decimal number (- 30 ) as an 8-bit number in 2's complement form, an verifying its decimal value. B) Implement the Boolean function X = CD + CD + ABD using only NAND gates. %3D
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Q: AAo 00 9. AIAO A3A> 01 %3D 10 A3A 00 00 00 16 10 b= A3 A, Ao + A3 AIAO
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![C) Show how the expression can be implemented as stated using only NOR gates:
X = AB[C(DE + AB) + BCE]
Q3: A) Express the decimal number (- 30 ) as an 8-bit number in 2's complement form, and
verifying its decimal value.
B) Implement the Boolean function X = CD + CD + ABD using only NAND gates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31bbe849-a150-4729-95c8-4124e1381d3c%2Fef12b204-6e0e-4dbe-9ce7-0d8f22b61f9b%2Fbq5b6hc_processed.jpeg&w=3840&q=75)
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- A majority gate is a digital circuit whose output is 1 only if the majority of inputs are 1 otherwise the output is 0 for all other cases. Design a combinational logic circuit for 4-input majority gate. a. Construct the Truth table. b. Minimize POS Expression using K MAP c. Draw the combinational circuit for minimize POS4. A combinational logic circuit that compares between two 2-bit numbers A (AI A0) and B (B1 B0) is designed. Output F is high when A > B and low when A < B. a. Are there any conditions which cause none of the outputs to be asserted? If the conditions exist, what are the inputs? b. Derive the truth table and obtain the maxterm notation for the output. c. Obtain the minimized POS expression of the logic circuit. d. Draw the logic circuit using basic gates.Implement the Logic expression using only NOT and two-input NAND gates. A+B+C+D
- Show the Ladder logic program and the equivalent Function Block Diagram for the following Boolean expressions without any simplification: - 1) Y= A.B+C+(C+B). D 2) Y= A.B.C+B.D. (AOP)+C 3) Y= A.B (C + D) + D+ A BConsider F(A,B,C) = AB'C + B'C' + A'BC + A'C' 1. Determine how many logic gate inputs would be needed before any simplification. Do not count inputs to NOT gates 2. Use Boolean algebra rules to get the most simplified expression of F(A,B,C). Then determine how many logic gate inputs would be needed after simplification. Again, do not count inputs to NOT gates. 3. Expand the original expression into its canonical SOP representation. 4. Fill out the K-map below using the SOP canonical representation. Group the 1-cells according to the K-map simplification rules. Translate each group into its product term, OR these product terms together, and verify that the expression you get matches the one in Step 2. 5. Draw two circuits in CircuitVerse, one from the original expression for F(A,B,C), the other from the simplified expression in Step 2 or Step 4. Connect the inputs to both circuits, but separate their outputs. Verify through simulation that these two circuits are indeed equivalent. Take…1. a. i. Draw the gates required to build a half adder are ii. When simplified with Boolean Algebra (x + y)(x + z) simplifies to : iii. The output of a logic gate is 1 when all its inputs are at logic 0, the gate is either :
- 2. The Boolean Algebra expression is given as Q = Ā(BC + BC + BC) + ABC a. Convert this logical equation into an equivalent SOP term. b. Use a truth table to show all the possible combinations of input conditions that will produce the output Q. c. Draw a logic gate diagram for the expression. d. Simplify the expression Q using Boolean Algebra. e. Draw the logic gate diagram of the simplified output Q.Assuming we are given a Logic Gate network, the output of the circuit is given by the following equation Q=A.B+A.C+ A.B.C By using the Boolean Logic rules for simplification, select which of the following equations is the correct simplified one. Note that, the answer None of the above may sometimes be the correct response. Q=A+(B.C) O Q=A.(B.C) O Q=Ā. (B+C) ⒸQ=A. (B+C) None of the above O Not answeredThe 4221 code is a base 10–oriented code thatassigns the weights 4221 to each of 4 bits in a nibble ofdata. Design a logic circuit that takes a BCD nibble asinput and converts it to its 4221 equivalent. The logiccircuit should also report an error in the BCD input ifits value exceeds 1001.
- 8) Draw a logic circuit to implement the Boolean function F and with only NOR gates (AC+AB+BC)Draw the equivalent logic circuit diagram of the following expressions : a. XY = F b. X + Y = F XÝZ = F c. d. XY + XZ = F e. XYZ + XÝZ = FImplement the Boolean function F= A.B.C + A' + A.B'.C using logic gates.