Homework Answers
Answer) (A) x'y + x
We Form SOP equation through those varables in tables whose result F is 1. There are 6 rows with F=1. We pick these to form SOP and if x=0 then it is written as x' and if x=1 then it is written as x. similarly for y and z. See solution below:
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Question 10 5 pt Which of the following expression is a minimum SOP (Sum-of-Product) expression for...
Question 10 5 pts Which of the following expression is the correct minimum SOP (Sum-of-Products) expression...
Question 10 5 pts Which of the following expression is the correct minimum SOP (Sum-of-Products) expression of the function F shown in the truth table below? X 2 F y 0 0 0 2 1 0 0 0 0 0 0 0 1 شما 0 1 1 1 0 2 5 6 7 0 0 0 1 1 1 0 1 1 1 1 1 Yz' + x2 + xy yz' + x2 yz + xy yz + xy+ xy'z...
Question 20 (5 marks) For the truth table shown below in Table 1, A C X...
Question 20 (5 marks) For the truth table shown below in Table 1, A C X 0 C C 1 0 C 1 1 0 1 C 1 0 1 1 0 1 0 C 0 1 0 1 0 1 1 C 0 1 1 1 Table 1 a) Derive the standard Sum Of Product (SOP) expression (1 mark) b) Derive the standard Product Of Sums (POS) expression. (1 mark) c) Use a Karnaugh map to find the minimum...
#1,2,7,9 Fall 2019 Test 2 Practice Problems EE210 m(1.6.7). Use a K-map to simplify the Show...
#1,2,7,9
Fall 2019 Test 2 Practice Problems EE210 m(1.6.7). Use a K-map to simplify the Show a truth table for the function F(w, x, y)= function. Find a minimal AND-OR realization 2. Using a 3.variable Karnaugh map, find a minimum SOP reduction for F(A,B,C) - m(0,1,5,7). Using a 4-variable Kamaugh map, find a minimum SOP reduction for F(A.B.C.D) - Ym(1.5.7.11.13.15) Using a 4-variable Karnaugh map, find a minimum SOP reduction for F(A,B,C,D) - Sm(1.5.7,11,13,15) + d(2,3) Study Guide, Unit 5....
Question 2 1. Formulate the minimized SOP and POS Boolean expression for the following truth table...
Question 2 1. Formulate the minimized SOP and POS Boolean expression for the following truth table using Karnaugh map techniques. Out of the SOP and POS implementations, which is cheaper in terms of number of transistors? You can assume two transistors per input for a gate. (10 points) A B C Output 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A...
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A + BC + CD (b) ABCD + ABCD + ABCD + ABCD (c) ABCD + CD) + ABCD + CD) + ABCD (d) (AB + ABXCD + CD) (e) AB + AB + CD + CD 2. Use K-maps to find the minimum SOP expression for the logic function shown in the table to the right. Implement the circuit using NAND gates only. Inputs...
Question 4. (a) Find the minimum sum-of-products expression for each of the functions below using Karnaugh...
Question 4. (a) Find the minimum sum-of-products expression for each of the functions below using Karnaugh maps i) F = EA,B,C,D(2, 3, 6, 7, 12, 13, 14) (Note: the numbers in the brackets correspond to positions in the Karnaugh map where F takes the logic value 1, ie F = 1 when ABCD = 0010, 0011, 0110, etc). ii) F = []w.x,y,z(0, 2, 6, 7, 8, 14, 15) (Note: the numbers in the brackets correspond to positions in the Karnaugh...
Please provide all requirements of the question, including truth table (if any). Please include the SOP...
Please provide all requirements of the question, including
truth table (if any).
Please include the SOP and the POS forms for both
functions.
1. Find the minimum sum of products and product of sums expressions for the following functions using k-maps. F(ABCD) = TM (2,5,7,8,9,10)d(3,4,11,12) F(WXYZ) = m(0,3,5,7,9,10,12,13) + d(1,6,11,14)
5. Apply Boolean algebra theorems to minimize the following expression. x(y + xy) + xy(x +...
5. Apply Boolean algebra theorems to minimize the following expression. x(y + xy) + xy(x + yy) 6. Consider the following digital circuit diagram. Write the corresponding logic expression for f and the truth table. D A $(91, 02, ) f(x1, X2, X3)
Given the function : F = x + ( (yz)’(x’ + y’+ z’) )’ A) Write...
Given the function : F = x + ( (yz)’(x’ + y’+ z’) )’ A) Write the truth table of F. B) Draw the K-map for F. C) Using the K-map, write the fully simplified Sum-Of-Products expression for F. D) Write the fully simplified product-of-sums expression for F
1) Implement each side with gates, that is a block diagram/schematic a+(b+c) = (a+b)+c a(b+c) =...
1) Implement each side with gates, that is a block diagram/schematic a+(b+c) = (a+b)+c a(b+c) = ab + ac 2) Make a truth table for each of the functions below and identify where each term comes from in the truth table a. F=X’Y+Y’Z’+XYZ b. G=XY+(X’+Z)(Y+Z’) c. H=WX+XY’+WX’Z+XYZ’+W’XY’ 3) For the expression F = A’B’C + ABC + ABC’ How many literals are there ___________ How many terms are there ___________ 4) F(a,b,c,d) = m(0,1,4,7,12) Find the canonical sum (which is...
Question 10 5 pts Which of the following expression is the correct minimum SOP (Sum-of-Products) expression of the function F shown in the truth table below? X 2 F y 0 0 0 2 1 0 0 0 0 0 0 0 1 شما 0 1 1 1 0 2 5 6 7 0 0 0 1 1 1 0 1 1 1 1 1 Yz' + x2 + xy yz' + x2 yz + xy yz + xy+ xy'z...
Question 20 (5 marks) For the truth table shown below in Table 1, A C X 0 C C 1 0 C 1 1 0 1 C 1 0 1 1 0 1 0 C 0 1 0 1 0 1 1 C 0 1 1 1 Table 1 a) Derive the standard Sum Of Product (SOP) expression (1 mark) b) Derive the standard Product Of Sums (POS) expression. (1 mark) c) Use a Karnaugh map to find the minimum...
#1,2,7,9
Fall 2019 Test 2 Practice Problems EE210 m(1.6.7). Use a K-map to simplify the Show a truth table for the function F(w, x, y)= function. Find a minimal AND-OR realization 2. Using a 3.variable Karnaugh map, find a minimum SOP reduction for F(A,B,C) - m(0,1,5,7). Using a 4-variable Kamaugh map, find a minimum SOP reduction for F(A.B.C.D) - Ym(1.5.7.11.13.15) Using a 4-variable Karnaugh map, find a minimum SOP reduction for F(A,B,C,D) - Sm(1.5.7,11,13,15) + d(2,3) Study Guide, Unit 5....
Question 2 1. Formulate the minimized SOP and POS Boolean expression for the following truth table using Karnaugh map techniques. Out of the SOP and POS implementations, which is cheaper in terms of number of transistors? You can assume two transistors per input for a gate. (10 points) A B C Output 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1
1. Use K-maps to reduce each of the following to a minimized SOP form: (a) A + BC + CD (b) ABCD + ABCD + ABCD + ABCD (c) ABCD + CD) + ABCD + CD) + ABCD (d) (AB + ABXCD + CD) (e) AB + AB + CD + CD 2. Use K-maps to find the minimum SOP expression for the logic function shown in the table to the right. Implement the circuit using NAND gates only. Inputs...
Question 4. (a) Find the minimum sum-of-products expression for each of the functions below using Karnaugh maps i) F = EA,B,C,D(2, 3, 6, 7, 12, 13, 14) (Note: the numbers in the brackets correspond to positions in the Karnaugh map where F takes the logic value 1, ie F = 1 when ABCD = 0010, 0011, 0110, etc). ii) F = []w.x,y,z(0, 2, 6, 7, 8, 14, 15) (Note: the numbers in the brackets correspond to positions in the Karnaugh...
Please provide all requirements of the question, including
truth table (if any).
Please include the SOP and the POS forms for both
functions.
1. Find the minimum sum of products and product of sums expressions for the following functions using k-maps. F(ABCD) = TM (2,5,7,8,9,10)d(3,4,11,12) F(WXYZ) = m(0,3,5,7,9,10,12,13) + d(1,6,11,14)
5. Apply Boolean algebra theorems to minimize the following expression. x(y + xy) + xy(x + yy) 6. Consider the following digital circuit diagram. Write the corresponding logic expression for f and the truth table. D A $(91, 02, ) f(x1, X2, X3)
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