Design a digital circuit with the minimum number of gates with the 4-bit input A = a3a2a1a0and the 4-bit output B = b3b2b₁bo. Your design must be according to the followingspecifications- If A is 0, then B must take a don't care value.- If A is divisible by both 3 and 5, B must take a don't care value.- If A is divisible by 3 but not divisible by 5, then B = A ÷ 3.- If A is divisible by 5 but not divisible by 3, then B = A ÷ 5.-If A is not divisible by either 3 or 5, then B = A × 3. If this multiplication result exceedsthe maximum allowed range value, then B must be replaced with a don't care value.a. Plot a truth table, K-maps, and derive the corresponding logic diagram. (Assume variablesand their complements are available). Your diagram must be a single circuit producingall output bits of B.b. Redraw the logic diagram of the circuit using only NAND gates. (Assume variables andtheir complements are available)c. Redraw the logic diagram of the circuit using only NOR gates. (Assume variables andtheir complements are available)

Answered: Design a digital circuit with the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Given a 4-bit signed integer, design a circuit that outputs its absolute value. You can assume that the input will always have a valid output. (a) Draw a logic diagram of this circuit. You may use 4-bit half adder(s), 2x1 4-bit multiplexer(s), and any logic gate(s) in your design. (b) With the following Verilog code, implement your design above in Verilog. module half_adder (input [3:0] a, input [3:0] b, output [3:0] s); assign s = a + b; endmodule module mux(input [3:0] D0, input [3:0] D1, input S, output reg [3:0] O); always @(*) begin if (S == 0) O = D0; else if (S == 1) O = D1; else O = 4’bx; end endmodule
Part a Design a logic circuit using the truth table Inputs output shown. Use only basic logic gates (AND, OR, NOT). Also, the circuit should use the FEWEST number of gates and the FEWEST number of inputs to the gates. Fully label all the inputs and outputs. a b. 1 1 1 1 1. 1 1 Part b Implement a 3-input XOR gate using only a 4x1 multiplexer and an inverter. Also complete the truth table in your answer sheets with the correct labels and function solution. Fully label all inputs and outputs. Part c Design a full-adder using half-adders and A- additional logic using the half-adder shown here. Pi Gi
Given the expression F(X,Y,Z)= XY + Z, draw the circuit using NOT and OR gates only. How many NOT and OR gates will be needed? O 3 NOT and 1 OR O 2 NOT and 2 OR O 2 NOT and 1 OR 1 NOT and 3 OR O 1 NOT and 2 OR
Design a combinational circuit with three inputs x, y, and z, and three outputs, A, B, and C. When the binary input is 0, 1, 2, or 3, the binary output is one greater than the input. For example, if the inputs are 000, the outputs are 001. When the binary input is 4, 5, 6, or 7, the binary output is two less than the input. For example, when inputs are100, the outputs are 010. Show the truth table for the inputs and outputs. please show all steps , dont just explain
| A combinational circuit is specified by the following Boolean function: F(x, y, z) = E(2,4,6, 7) Implement the circuit with a decoder and external gates.
2. Consider the circuit below. a. Write the Boolean expression for output F in terms of A, B and C. b. Construct a truth table for the circuit with A as MSB and C as LSB. c. Write the Canonical SOP and POS forms for output F. A B C 3. Draw the logic circuit represented by the expression F(A, B) = AB using no more than 5 units of 2-input NAND gate and write the corresponding Boolean expression.
Design a logic circuit whose output is HIGH only when a majority of inputs A, B, and C are LOW. Draw the circuit using all NAND gates.
Design a combinational circuit with three inputs x, y, and z and three outputs F1, F2, and F3 with the minimum possible number of gates, based on the following specifications: ⚫ The output F1 is 1 when the binary value of the inputs (the 3 bits together) is equivalent to a decimal number that is less than decimal 4, otherwise the output is 0. ⚫ The output F2 is 1 when the binary value of the inputs (the 3 bits together) is equivalent to a decimal number that is either 4 or an odd decimal number, otherwise the output is 0. ⚫ The output F3 is 1 when the binary value of the inputs (the 3 bits together) is equivalent to a decimal number that is either 0 or greater than decimal 4, otherwise the output is 0. a) Your design steps must include: A truth table, K-maps, simplified Boolean expressions in canonical and standard SOP forms, and implementations with logic gates. Combine the logic diagrams into a single logic circuit having 3 inputs and 3 outputs. In your implementations, assume the…
Give the output signals for the circuit if the input signals are as indicated. R = P Q OR NOT input signals: P = 1 and Q = 1 AND R
A Design Combinational circuit that has 4 inputs and one output. its output should satisfy the following topak= even. -otherwise Then implement it using one MAWD gate only. t 2
Construct the circuit ¯x + y from inverters, AND gates, and OR gates to producethese outputs.
Draw the circuit schematic for f = xỹ + yz and then convert the schematic to NAND gates using the steps illustrated in the textbook.

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