Problem: Derive the logic expressions for a circuit that compares two unsigned numbers: X = x2x₁x0 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.
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- Consider the multiplexer based logic circuit shown in the figure MUX MUX 1 Select one: a. W S1' S2' O b. W + S2 + S1 c. WS1 + WS2 + S1 S2 O d. WeS1es2Draw 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 = FA circuit for adding two 3-bit 2's complement numbers (X2X1Xo and Y2Y1Y0) that uses Full Adder (FA) components is shown below. Write the full logic expression to detect overflow. Cout C3 X₂X₁ Xo FA Cir Cout C₂ Cout FA C S Z₂ Z₁ (Y₂) (Y₁ Yo Zo C₁ Cout FA Cin
- Design 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. For the logic circuit shown in Figure below write the required input condition (A,B,C) to make the output X =1. A BQ1. 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 CTask 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'C(a) A logic circuit shown in Figure Q.3 has a 4-bit input A and B, three 4-bit wide 2:1 muxes, a 4-bit adder, a 4-bit output F, and a carry flag C. For the given Table Q.3, fill in the value of output F and carry flag C for the given value of A, B, S0, S1 and S2. 51 52 1001 Flag C 0011 Figure Q.3 Table Q.3 A So S1 S2 F Flag C 0001 1000 0010 1001 1 1 0011 1101 0100 1101 1110 0111 1
- 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.A three input logic functipn will provide a logic high output only when twp (and two only) of the inputs are logic highs. For all other input possibilities, a logic zero is provided on the output. What is the logic expression? A. Y=A'B'C+A'BC'+AB'C' B. Y=AB'C+A'BC+ABC' C. Y=AB'C+ABC+A'B'C' D. Y=ABC'+AB'C+A'B'C'Design a combinational circuit with four input lines that represent a decimal digit in BCD and four output lines that generate the 9's complement of the input digit. Provide a fifth output that detects an error in the input BCD number. This output should be equal to logic 1 when the four inputs have one of the unused combinations of the BCD code. Provide a schematic logic diagram of it. It will surely help me in my review. Thank you so much!