Example: Design a 4-input (A,B,C,D) digital circuit that will give at its output (X) a logic 1 only if there more ones than zeros in the binary number formed at the input. Inputs Output X = АвсD 00 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 5 0 1 CD АВ 00 01 11 10 1 1 4 00 1 0 1 01 6 1 1 11 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 7 8 1 10 9 1 10 1 11 1 12 1 13 1 14 1 15 1 1 X = 1 1 1 1 A B 23
Q: A D
A: In the given logic circuit: A = X’ B = (AY)’ C = (Y ⊕ Z)’ D = (B + C)’
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- A combinational circuit with four inputs (A,B,C,D) and one output (Z) is designed as follows using an 8:1 multiplexer. Inputs A,B,C are connected to the select lines ?S2, S1, S0 respectively. Multiplexer has the following values connected to the data inputs: I0,I6 =1; I1,I3 =D; I2,I5 =0; I4,I7 =D’ Write the simplest logic expression of the circuit realized above Z= f(A, B, C, D)Design a combinational logic circuit that takes a 3–bit input and has one output P. The P output should be active high only when the inputs corresponds to a prime number Note: the prime numbers: Prime numbers are 2, 3, 5, 7… Select one: a. P= AC+B b. P= A'C+A'B c. P= AC+A'B d. P= AC+A'B'Truth Tables and Logic Gates /Circuits~ - NOT1. Derive truth tables for the following Boolean expressions:a) ~(A + B)b) ~ A + (~ B)c) (~ A) + Bd) (~ A). (~ B)e) (~ A). (A + (~ B)) 2. Derive truth tables for:a) A.B + (~C)b) A. (BC)c) (AB).Cd) (~ A) .(B + C)e) ~(AB) + C 3. Derive truth tables for the following; inputs are A, B and C.a) W is True if an even amount of inputs is True, and False otherwise.b) W is True if exactly one input is true, and False otherwise.c) W is true if A and C are the same, and False otherwise. 4. Draw the logic circuits for the following Boolean expressions:a) W = (AB) + (NOT C)b) X = (~A). (B + C)c) Y = ~(AB) + C
- A sequential circuit is represented by the state equations and the output functions asgiven belowA(n+1) = C'x + A' BB(n+1) = B'(C+Ax')C(n+1) = ABx+B'xand y=BC+A'x z=ABx'+A'C where x is an external input and y and z are external outputs.a) Obtain the state table of the sequential circuit.b) Design the sequential circuit given above using JK flip-flops.1a. Draw a circuit diagram using appropriate logic gates to implement a 3-bit comparator. Identifythe gates used in implementation and show its usage to compare two 3-bit words by writing thetruth table. b. Write the Boolean expression for the following 4 input circuit. Include sub-expressions foroutputs of each gate. c. Complete a truth table for the previous logic gate circuit in part b. d. Write the Boolean expression for the new circuit below. Then, simplify the following logic circuitusing the theorems in Boolean algebra. Show the steps clearly and specify the law used in eachstep. Finally draw the simplified circuit diagram.A combinational logic circuit has inputs A, B, C, D and E. The output Y is given by: fΠ M(15,31) where A is the Most Significant Bit. Give Y in terms of inputs A, B, C, D and E in a Product of Sum format.
- Create a logic circuit using only basic gates such as AND, OR, NOR, NAND, NOT, etc. to implement a Subtractor that is capable of subtracting the second number from the first, by converting the second number into its 2's complement form and then adding the resulting number to the first number. You do not need to worry about accomodating the addition or subtraction of negative numbers. Also, create a limited ALU (Arithmetic logic unit) circuit using Logism that implements a Full Adder circuit capable of adding 2 – 4 bit binary numbers and subtracting 2- 4 bit binary numbers. Also, implement the ability to select a bitwise AND operation and a bitwise OR operation. For the ALU it is acceptable to use the Adder and Subtractor circuits that are listed under the "Arithmetic" folder in Logism. (Logism tips and tricks are useful here for multi-bit pins, and how to set up different gates to support more than 1 bit. If using YOUR adder or subtractor circuit in your ALU that is not only acceptable…Computer Science: Give the correct answer with the correct work being shown You have been asked to implement a digital circuit. This circuit consists of threeinputs (X1, X2, and M) and one output (OUT). When M equals 1, OUT will equal theBoolean OR of X1 and X2. If M equals 0, OUT will equal the Boolean AND of X1 and X2.a. Construct a truth table to describe the behavior of the circuit.b. Write the sum-of-products for OUT.c. Provide an implementation of your sum-of-products. You are to use AND, NOT, andNOR gates only.In a sequential logic circuit, the next output is dependent on the inputs and the one before it. O a. Ob The only input is the clock signal. The background of the OC inputs. All we have is Od as input.
- subject: Digital Logic &Design Q: For the 4-input multiplexer, data inputs are givenas: D0 = 0, D1 = 1, D2 = 0, D3 = 1Find the output Y if the select inputs are given as:a)S0 = 1, S1 = 0b)S0 = 0, S1 = 1c)S0 = 1, S1 = 1d)S0 = 0, S1 = 0This is a computer architecture problem. Please explain clearly, no cursive writing. A logic design has 4 inputs called A, B, C, and D. The logic design has one output called F. A and B are the inputs to a NOR gate N1. C and D are the inputs to a NOR gate called N2. The output of N1 and the output of N2 themselves are inputs to a third NOR gate called N3. F is the output of N3.a) Give the truth table for this logic design showing A, B, C, D, and F b) Which of the following logic expressions is equivalent to the logic design for this problem:i) (A OR B) AND (C OR D), ii) (A AND B) OR (C AND D), iii) (A AND B) AND (C AND D)Describe the function of a decoder circuit; A decoder circuit is a digital logic component that converts a binary input code of 2n bits into a maximum of unique output lines, with each output line corresponding to one of the possible combinations of the input code. It "decodes" the binary input into a one-hot (also called one-out-of-n) code, where only one output is active (high) at a time while all others are inactive (low). The primary function of a decoder is to detect specific combinations of inputs and assert the corresponding output line Identify the types and quantity of gates needed to implement a 3-to-8 decoder. To implement a 3-to-8 decoder, you need: -Three NOT gates to invert the three inputs if the decoder does not have enable inputs and the implementation requires all minterms. -Eight AND gates, each with three inputs, to generate the eight possible minterms corresponding to the eight different combinations of the three input bits. So, in total, you…