Design a system that takes a 4-bit binary number ABCD as its input and whose output X is "1" if the decimal value of the input is equal to any of these digits (1,3,4,8), then output = 1 if the decimal value of the input is 0. A. Define your input variables and output variable and identify the relationship of the variables B. Generate a truth table C. Formulate a logical expression in canonical form D. Simplify your logical expression using the minimum number of literals, if possible. Make sure to write the Boolean property/law that was done per step of simplification.

Design a system that takes a 4-bit binary number ABCD as its input and whose output X is "1" if the decimal value of the input is equal to any of these digits (1,3,4,8), then output = 1 if the decimal value of the input is 0. A. Define your input variables and output variable and identify the relationship of the variables B. Generate a truth table C. Formulate a logical expression in canonical form D. Simplify your logical expression using the minimum number of literals, if possible. Make sure to write the Boolean property/law that was done per step of simplification.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Similar questions

Implement the given product of maxterms expression Y(A, B, C)= ΠM (0, 1, 2, 4, 5) using a PROM. (a) Write the sum of minterms expression (b) Write the truth table for the expression in (a) (c) Draw the diagram of PROM showing the programming.
Simplify the given Boolean expressions, using four-variable map. Provide clear solution. A'B'C'D' + AC'D' + B'CD' + A'BCD + BC'D
Assuming (47) based 10 = (abcdefg) based 2, consider the Boolean function F(A, B, C, D) given by the following truth table for all the questions: a) Implement F (ABCD) using 3x8 Decoders with ‘Active High’ output and Enable inputs and external gates,b) Implement F (ABCD) using 3x8 Decoders with ‘Active Low’output and Enable inputs and external gates,c) Is it possible to implement F( ABCD ) with decoders using logic gates with smaller number of inputs than given in part a) or part b)?
Simplify the following Boolean expressions, using four-variable K-maps: A′B′C′D+AB′D+A′BC′+ABCD+AB′C
Use KARNAUGH Mapping to obtain the Simplest Boolean Expression. Use standard Sum-of-Product (SOP). Show complete and detailed workout
Simplify the Boolean function F(w, x, y, z) = summation(3, 4, 5, 8, 11, 12) +d(1, 10, 13) using the tabular method.
A lottery system consists for 4 different numbers combination. Following are different winning combination • All FOUR numbers match • If THREE numbers match including 1st number • If FIRST TWO numbers match (a) Set–up the truth–table (b) Derive the output expressions (c) Simplify the derived expressions (d) Implement the simplified digital logic circuit, using LogiSim.
use KARNAUGH MAP method to minimise for the simplest Boolean expression. Use standard Sum-of-Product (SOP). Show complete and detailed workout
Represent the following Boolean functions in simplest possible form in both Sum of Product (SOP) and Product of Sum (PoS) formats, F (a,b,c,d) =π(1,2,3,5,13,14) d (w.x.v.z)=£(0,4,5,7,14) Note: Minimize the expressions by using K-Mop
Digital Logic Design503221-4 Assignment 2[1] Consider a Boolean Algebra <B,+,.,0,1> Show that(a) x.y + x'.z + yz = x.y + x'.z(b) (a + b)'(a' + b)' = 0[2] Algebraically simply the following expressions:(a) F = abc + a'bc + a'b'c +abc' + a'b'c'(b) F = y(wz' + wz) + xy[3] Simplify the following Boolean expressions to a minimum number of literals :(a) ?? + ??̅(b) (? + ?)(? + ?̅)(c) ??? + ?̅? + ???̅(d) ( ̅̅?̅̅+̅̅̅?̅̅̅) (?̅ + ?̅)[4] Reduce the following Boolean expressions to the indicated number of literals :[5] Find the complement of the following expressions :(a) ??̅ + ?̅?(b) (? + ?)(? + ?̅)(?̅ + ? + ?̅)(c) ? + ?̅(?̅? + ??)(d) ( w + y̅z)( x + w̅z)[6] Given F = ab + b(ad ̅̅̅ + ac̅) implement it with AND, OR and inverter gates.[7] Implement the Boolean function? = ?? + ?̅? (a) ?̅?̅ + ??? + ??̅ to three literals.(b) (̅̅?̅̅̅?̅̅̅+̅̅̅?̅̅) + ? + ?? + ?? to three literals.(c) ?̅?(?̅ + ?̅?) + ?(? + ?̅??) to one literals.(d) (?̅ + ?)(?̅ + ?̅)(? + ? + ?̅?) to four literals.(a) With AND, OR,…
Course: DigitalLogic Design Please solve this question in a 2 hour. Solve it step by step clearly: Question: Simplify the following to the least of literals using Boolean Algebra: F(x,y,z)= xyz' + xy'z + x'y'z' + x'yz' Draw logic diagram of the circuit that implement the original and specified expression above. Also draw the truth table for both expressions.
Simplify the expression with four variable using various Boolean algebra Q= ?(0,3,4,7,10,12,14).Draw the Circuit in logisim with minimum hardware.(Using SOP).