(a) Write the Truth Table for the Boolean expression X = E m ( 0, 2, 3, 4, 5 ) 1. Write the POS expression for this truth table as a function of input variables. (2 marks) (b) For a two-input NAND gate, Find the standard SOP and POS expressions as a function of input
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- (a) Simplify the following Boolean expression 'A' and draw the logic diagram for the simplified expression. A = (X + YZ) + (X Y ) (b) Convert the given standard SOP expression, Y(A, B, C)= Em (0, 1, 2, 3, 5) into standard POS expression. (c) Draw the block diagram of 4 to 1 Multiplexer and write its truth table. (Note: The handwritten solution for all parts of this question with all steps should be scanned, and uploaded to Moodle via the submission link).A) Find the Boolean Equation for the following circuit and Simplified Boolean Equation? B) Find 8 bit representation of (-1)-Create the logic for a ene bit addition circuit. Inputs are X, Y, Cio, Xand Y are the bits being added. Çigis carry input to be added to sum of X, Y. Outputs are Sum (sum af XX, Çip) and Caut (carry from the whole addition). Write an expression for each output using ginter natation. i Ue a truth table to mag all pobie combinations of tte inputs to the outputs. Create SDP apreuions from thetruth table. Tou may u eiter algetraic ar qvnstatian. If you un ntow the order of the wariaa Sum (X, v, bol = Emt
- Using Boolean algebra theorems, simplify the logic expression above as far as possible. Create a Circuit Diagram for the new expression Then create a truthtable for the simplified circuitB/ Show the required steps to derive a Boolean expression in a simplified SOP form for the output Z of the following logic circuit A B Csimplify this expression using boolean expression simplification. (the other solution is in incorrect input)
- Given the below terms of the logic expression. F(A, B, C, D) = (2,4,7,10,12); d(A, B, C, D) = (0,6,8) 1. Obtain the KMAP to get minterms and maxterms. 2. Provide the Simplified Boolean Function. (Example: F = A) 3. Generate the Logic Diagram of the Simplified Boolean Function.A shaft position encoder has 4 output. The outputs corresponding to each position are given in thetable below. It is desired to design a circuit thatshaft position between and → the output f=1at the other position → f=0The values not determined by the shaft position will be taken as 0.a) Fill the truth table. b) Reduce the output function as sum of minterms using Karnaugh map. c) Realize this function using logic gates.You are asked to construct a multi-function shift register with the functionality shown**: A. Design a one bit circuit which implements the functionality. Use D flip flops and any logic gate and/or combinatorial circuit seen in class. Label all inputs and outputs. B. Use the one-bit circuit from (A) to implement a four bit shift register. Use the principal of abstraction to represent each instance of the circuit from (A) as a functional block. Clearly label all ports.
- A digital circuit for adding two binary digits has two inputs: the two digits to be added; and two outputs: the units bit and the twos bit of the answer. (a circuit of this kind is called half adder.) By treating this as two circuits, each with a single output, use Karnaugh maps to obtain a Boolean expression for each circuit, and draw the corresponding circuit diagrams.Create a truth table with four inputs A, B, C and D and one output, Y. The output is FALSE only when A B and C=D. Otherwise the output is TRUE. Draw the Kamaugh map. write the simplified SOP expression and sketch the gate-level schematic.Discuss briefly the following Boolean Algebra terms and give at least five (5) examples each : a. Sum of Products (SOP) b. Product of Sums (POS)