(a) Write the Truth Table for the Boolean expression X = Em (0, 1, 2, 4, 5) Write the POS expression for this truth table as a function of input variables. (b) For a two-input EX NOR gate, write the truth table and find the standard SOP and POS expressions as a function of input variables.
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- 4 Design a combinational logic circuit that accept (2-bit) mumber (A) and generate an output binary mumber (X) equal to the square of input (X - A) a. List the truth table. b. Write the Boolean expressions for the output (X). c. Draw the logic circnit.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.Task One: Air conditioning (AC) control system Design a simple AC control system that receives a signal from a digital thermometer sensor. Depending on the room temperature, the signal will control the air conditioner to operate in Heating, Ventilation, or Cooling modes. The digital thermometer signal produces a 4-bit binary number proportional to temperature, where 0000 represents 0 degrees and 1111 represents 48 degrees (so each binary number represents a multiple of 3 degrees). Consider the following specifications in your combinational logic circuit design: Whenever the temperature is less than T₁, the AC should operate in Heating. Whenever the temperature is greater than T2, the AC should operate in Cooling. Whenever the temperature is between T₁ and T2, the AC should operate in Ventilation. Where: T₁ = 14 + (your last digit of your university ID) mod 4 degrees T₂ = 17+ (your last digit of your university ID) mod 4 degrees
- Simplify the the Boolean expression as best as possible, show step by step solution and prove it with a truth table. Design the logic circuit of the simplified expression. 1.] ((A'BCD'+B'.C'D)'(A.B'))' 2.] (A+B+C')(A'+B+C')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 = EmtDraw a logic circuit for ?̅ ∙ ??. Create truth table for this expression. What logic gate is this equivalent to? What Boolean Algebra identity is it?
- 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 circuitPlease draw the logic circuit for the Boolean expression, attached. Do not simplify the expression.4. A combinational logic circuit has four inputs and one output. The output is 1 if and only if the decimal number represented by the inputs in binary code is a prime number. i. Construct the truth table and simplify the Boolean expression into POS form using K-map. ii. Construct the logic diagram using OR-AND gate network with simplified POS expression iii. Construct the logic diagram using only NOR gates with simplified POS expression.
- Write the expression “G. Boole” in ASCII, using an eight-bit code. Include the period and the space. Treat the leftmost bit of each character as a parity bit. Each eight-bit code should have odd parity. (George Boole was a 19th-century mathematician. Boolean algebra, introduced in the next chapter, bears his name.)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.A.Get the Boolean expreession of each output variable B. Simplify the three output boolean expressionC. create a circuit using the simplified boolean expression