Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 15.4, Problem 1E
Program Plan Intro
To determine the LCS ofthe sequences
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:Use Karnaugh map to simplify the following Boolean expression :
F(a, b, c, d, e) = [lm (0, 2, 6, 8, 12, 14, 16, 18, 26) + d (4, 9, 10, 24)
7. Write the simplified (minimized) expression for the Boolean function defined by the
following Karnaugh Map (KMap) in Sum of Product (SOP) form.
WX
yz
00
01
11
10
00
0
0
1
1
01
1
1
1
1
11
0
1
0
0
10
1
1
0
1
COMPUTER SCIENCE&IT
Write a simplified maxterm Boolean expression
for a (0, 4, 5, 6, 7, 10, 14) using the Karnaugh
mapping method.
Chapter 15 Solutions
Introduction to Algorithms
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5E
Ch. 15.2 - Prob. 6ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12P
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- Express the complement of the following function in sum of minterms: a) F (A,B,C,D) = Σ (0,2,6,11,13,14) b) F(x,y,z) = Π (0,3,6,7)arrow_forwardConstruct table of minterms and maxterms for 4 variables - x,y,z,w Obtain the truth table of the following functions, and express each function in sum-of-minterms (canonical SOP) and product-of-maxterms ( canonical POS) form: a) (xy+z)(y+x'z) b) (x+y)(y'+z) c) x'z+wx'y+wyz'+w'y' d) (xy+yz'+x'z)(x+z) Simplify the following Boolean functions T1 and T2 to a minimum number of literals: T2 0 0 0 1 1 1 1 1 A OOO 0 0 0 LLLL 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 اهای 1 T1 1 1 1 0 0 0 0 0arrow_forwardSimplify the Boolean function F(w,x,y,z) = (0,1,2,4,5,6,8,9,12,13,14)arrow_forward
- CREATING A CIRCUIT DIAGRAM Questions 4 and 5 refer to the function defined by the following truth table: w result 00001 00010 00110 00101 01101 01111 01010 0100 0 1 1000 1 1 0 1 0 1 111 0 11101 1 010 1 0 1 1 0 1 - 1 0010 1 000 1 Question 4 Fill in the values and draw the groupings of the Karnaugh Map. ५३ Wx 00 01. 11 10 00 01 11 10arrow_forward37. Write the standard product term for each cell in a 3-variable Karnaugh map. SECTION 4-9 Karnaugh MAP SOP Minimization 38. Use a Karnaugh map to find the minimum SOP form for each expression: (b) АC(В + С) (d) АBС + AВС + АВС + АВС (a) ABC + A BC + ABC (с) A(ВС + ВС) + A(ВC + ВС) 30 nimum SOP form:arrow_forwardSimplify the following Boolean function using sum-of-products format F(A,B,C,D) =E (0, 2, 3, 7, 8. 10. 11, 12, 13, 14, 15)arrow_forward
- Convert the following to the other conical form ( a) F (X Υ, )- 1.3,) (b) F (W,X, Y, Z) = II (0,1,2,3,4,6,12)arrow_forwardCreate the K-maps and then simplify for the following functions: 1) . F(x,y,z) = y′z′ + y′z + xyz′arrow_forward3. Use the Karnaugh-Map to simplify the following expressions F(A, B, C) = ABC + ABC + ABC + ABC + ABC F(A,B,C,D) = A + AB + ABC + BCD + ACD ii.arrow_forward
- Find the minterms of the following Boolean expressions by first plotting each function in a K-map: wyz+w′x′+wxz′arrow_forwardSimplify the following Boolean functions, using Karnaugh map:F(A,B,C,D) = ∑(0, 2, 4, 5, 6, 7, 8, 10, 13, 15)arrow_forwardQ3 A: Simplify the following Boolean functions, using Karnaugh maps: F (xy, z) Σ (0,1,4,5)arrow_forward
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