Answer Happy

Hello, my dear Could you please help me in these questions
fast
I do not understand you?
Simplification of Boolean Functions Objective: The objectives of this lab are to design and test a digital circuit starting from a given truth table, or from a given Boolean function. Students will learn about the importance of simplification, and how to express a function in sum of product (SOP) and product of sum (POS) forms using different methods. Equipment Needed: | Digital trainer with breadboard, switches, LEDs (light emitting diodes) and +5 V supply. | 1 Quad 2-input OR gate (7432) 1 Quad 2-input AND gate (7408) 1 Quad 2 input XOR gate (74 86) 1 Hex INVERTER (NOT gate), (7404 or 7414) 0 Digital logic probe is helpful Introduction: For an introduction to this subject refer to the lecture notes. Procedure: You must read this entire Lab Sheet, and follow all instructions below. Question 1: a) See Table 1 below for the truth table of a function Y: Table 1. Three-input, one output truth table for function Y с Y A B 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 b) Find the Boolean expression for Y in Sum-of-Minterms form.
c) Simplify Y so it is a sum of 3 product terms with 2 literals each to get Sum of Products (SOP). d) Draw the logic diagram for part (c). Hint: You must make a 3 input OR gate from 2 input OR gates. e) Choose which integrated circuits (IC) you will use to test this circuit. Label the gate inputs and outputs above with the appropriate pins for that package. See the last page for pin-outs. f) Assemble the logic circuit for the given expression using necessary ICS. DON'T connect power until your instructor sees your circuit! Use the toggle switches on the Digital Trainer for A, B and C inputs. | Connect the output to an LED on the Digital Trainer. g) Fill in the truth table below.
Table 2. Results of hardware testing for function Y. A B с Y 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 h) Is Table 2 the same as Table 1? i) Take a picture of your working circuit and put it in your lab report. Label the picture "Hardware for testing function Y" in your lab report (described below). Do the following in lab if there is time. If there is no time, then just to j, k, l, m, n at home and skip steps o, p, q, and r. j) See Table 3 below for the truth table of a function S: Table 3. Three-input, one output truth table for S S А с 0 0 0 <oooo Oo 0 1 1 0 1 0 1 0 1 1 1 0 0 1 ooo 1 0 1 1 1 0 0 1 1 1 1
k) Find the Boolean expression for Sin Sum-of-Minterms form and also find Sum of Products (SOP). 1) Simplify S and draw the logic diagram with only XOR gates. Lab Report Exercise: Question 2: Submit a lab report by including this lab handout with attached sheets as needed to do the following: You must read this entire Lab Sheet, and follow all instructions. 1). Express Y in POS form. Do this by first Y' and then simplify. Then invert this (Y')' to get Y in POS form. Prove it is correct with a truth table. 2). Express F=A'C + B'C'+AB I POS form. Prove it is correct with a truth table. 3). Include the pictures for part i in your report. Label them as described.
A+AB = A A(A + B) = A A+ A B = A+B = (A+B)(A+C) = A+BC A B A+B = A+ B = А В 7408 AND 7432 7404 / 7414 Hex Inverter 14 21 13 AO LA VCC VCC Ао 14 13 12 11 10 210 10 BO 3 3 12 12 G 5 C 4 5 11 10 - VCC •Az 03 A4 -04 -A5 -Og 00 A1 5 B1 011 fo A2 B2 02 A3 u uw N N 8 10 6 A2 72 GND 9 7 8 B3 03 | 2 3 GND GND 7486 B4 A4 A3 Y3 Vcc 14 Y4 11 83 10 7400 NAND gate 13 12 19 Vcc 14 1 2 3 3 4 5 6 GND A1 B1 Y1 A2 B2 Y2 GND