6. i) For the circuit shown in Figure Q16, Find the logic functions of X and Y Figure Q16 ii) Simplify X and Y using Boolean algebra.
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- 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 :An X-input exclusive-OR gate and a Y-input exclusive-OR gate (where X=3, Y=4 have their outputs connected to a 2-input exclusive-NORgate. Do the following:a) Draw the logic diagram and analyze the logic expression of the output (in standard SOPform).b) List out all essential prime implicants.Basic Combinational Logic Circuits 2. Write the output expression for logic circuit: A B B X
- Task 6: Simplifying Boolean functions in EWB using the logic converter Simplify the following Boolean expression in EWB using the logic converter F (A, B, C) = AB'C'+ A'B'C'+ A'BC'+ A'B'CDesign the following combinational logic circuit with a four-bit input and a three-bit output. The input represents two unsigned 2-bit numbers: A1 A0 and B1 B0. The output C2 C1.C0 is the result of the integer binary division A1 A0/B1 B0 rounded down to three bits. The 3-bit output has a 2-bit unsigned whole part C2 C1 and a fraction part CO. The weight of the fraction bit CO is 21. Note the quotient should be rounded down, i.e. the division 01/11 should give the outputs 00.0 (1/3 rounded down to 0) not 00.1 (1/3 rounded up to 0.5). A result of infinity should be represented as 11.1. A minimal logic implementation is not required. (Hint: start by producing a truth table of your design).4. Figure 2 shows a logic circuit with output F Figure 2. Logic circuit with gate I (AND), gate II (AND), gate III (NOT), gate IV (AND), gate V (EXOR) and gate VI (OR) a. Find the Boolean expression of output F. b. The simplified Boolean expression of Output F. c. If the input A and C were High and Input B was Low, what is output F:
- Consider two 8-bit inputs, A = $52 and B = $C3 to the arithmetic and logic unit (ALU). Compute R =A + B. Express R in the hexadecimal form $-- : -61 Express N-Z-V-C bits in the form ----:Design a combinational circuit with 3-inputs and 1-output. The output is equal to logic-1 when the binary value of the input is less than 3. And the output is logic-0 otherwise.For the input waveforms in Figure , what logic circuit will generate the output waveform shown? Explain in detail for each. Inputs B Output X Inputs B Output X
- Problem: Derive the logic expressions for a circuit that compares two unsigned numbers: X = x2x1xo and Y = = y2y1yo and generates three outputs: XGY, XEY, and XLY. One of these outputs is set to 1 to indicate that X is greater than, equal to, or less than Y, respectively.Q1. Determine the output waveform and Boolean expression X of the logic circuit in given circuit. D. B Q 2. Find the all Boolean expression for Y1, Y2, Y3, and Y4 (in the Q-1) and the intermediate waveforms at each of points Y1, Y2, Y3, and Y4.2.1 Combinational logic circuits. Tabulates a truth table for the following Boolean expression shown in Equation 1.1. f = A.B.C + A.B.C + A.B.C (1.1) 2.2 Half adder. A half adder is a circuit that adds two binary digits, A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. Figure 1.2 depicted a logic diagram for a half adder. a. derives the Boolean expression for s and c. b. tabulates a truth table for the half adder. Ao Bo Figure 1.2: Half adder os S C