Simplify the following expressions using Boolean Algebra properties and theorems. No needto specify the theorem names.a) F = [(A + B' + C') .(A' + B + C')]'b) Ya'bc abc' + abc + a'bc'a) Analyze the following combinational circuit and find the equation for y1 and y2 outputs.Express the equations in sum of product.aУт

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Answered: Simplify the following expressions…

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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5- For the Boolean function: F=XY'Z+X'YZ+W'XY+ WX'Y+ WXY (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
Draw the logic diagram corresponding to the following function: F = xy + (x+z) + x’ Simplify the function by using Logisim tools
VIII. Analyze the given truth table to find out the simplified Boolean expression using K-Map SOP method. Write down the number of AND gates and OR gates used in the simplified circuit. a) Finding of SOP Expression b) K-Мар Entry c) Find the Simplified expression d) Draw the logic circuit of the simplified expression e) Identify the number of gates used Input Output ABCDF(A,B,C,D) 0000 1 00|01 1 0|0|1|0 0|0|11 1 0|10|0 010|1 1 0|11|0 o|1|1|1 1 |1|0|0|0 10|0|1 1 10|1|0 1 101|1 1 110|0 1 110|1 1 1110 1
Simplify the following boolean function:
B1. Answer all the following questions: a. Write the Boolean equation of the output Z directly from the following circuit (do not simplify). A O b. Using Karnaugh map, simplify the following Boolean function F (show your grouping): F (A, B, C) = E (1,3,5,6,7) = A'B'C + A'BC + AB'C + ABC' + ABC
7. 1) Write a Boolean equation in sum-of-products canonical form for each of the following five truth tables. 2) Then minimize each of the Boolean equation, and 3) sketch a combinational circuit that implement the minimized Boolean equation using only NOT, AND and OR gates. (b) (e) (a) A B Y 0 1 1 1 1 THOOD OH OH 1 AOOOOHH А 1 1 B ооннос 0 1 1 C OHO 1 нонон Y 0 ононРЕНС 1 1 1 1 1 (c) A B C Y 0 OOOOHHHH 1 1 oor ННОон 1 1 1 0 OHOO 1 1 1 нонон 1 OH OOOOHH 1 1 1 1 1 1 (d) A O O O O O O OOHHdddd 0 1 1 1 1 1 1 BOO C в 0 0 0 OHHHH OOOOHH 0 1 1 1 C D 1 нноонноонноонно 1 1 1 1 1 1 1 1 1 1 1 1 OHOHOHOHOHOHOHOH 1 1 Y 1 1 1 1 1 0 HOHHOOHHHO HOOOOO 1 0 1 1 1 1 1 1 1 A B 0 O O O O OOOOHHHH 0 1 1 1 1 НННН0000ннннооо о 1 COOHH OOHH OOHH OOHH с D 1 0 1 1 TOTOHOHOHOHOHOHOO 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 Y 0 OOOHOOHdddHH OOOO 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1
Question 8: Draw the circuit that implements each of the following equations: B + AC' (W + Y)' + X' (B + A'D) + (BC)' (W' + XY)' + (VWX' + Z)'
Given is the following circuit with 4 inputs A, B, C, D and the output Y. (O denotes an inverter.) ABCD & 00 & & & =1 & & =1 & & & ≥1 Y a) Create the truth table for this circuit. b) Use a K-map to simplify this circuit. c) State a Boolean equation that describes Y based on your simplification.
1. A combinational circuit is specified by the three Boolean functions: F(A, B, C) = C(A' + B') + AC' + BC' G(A, B, C) = ABC + BC H(A, B, C) = A + B a. b. C. Create a truth table for the circuit. Simplify the expressions using Karnaugh maps. Draw the logic diagram for the circuit using the simplified expressions obtained in part b.
For the Boolean function F (w,x,y,2)= xy'z + x'y'z+ w'xy (a) Obtain the truth table. (b) Draw the logic diagram. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression (c) and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression (c).
For the Boolean function F (w,x,y,z)= xy'z + x'y'z + w'xy (a) Obtain the truth table. (b) Draw the logic diagram. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression (c) and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression (c).
Task 4: Simplifying Boolean functions Simplify the following Boolean expression F (A, B, C) = (A+C") +C (C.A' + (B.A) +C Draw the simplified Boolean expression using EWB. Find out the truth table of the circuit.

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