Simplify the following functions using Karnaugh maps.
1) E(A, B, C) = ∑m (0, 3, 5, 6)
2) F(A, B, C) = ∏M (3, 4, 6)
3) G(A, B, C) = ∏M (0, 3, 5, 6)
4) H(A, B, C) = ∏M (5, 6)
1) E(A, B, C) = ∑m (0, 3, 5, 6)
Simplify function:
E=A'B'C'+A'BC+AB'C+ABC'
2) F(A, B, C) = ∏M (3, 4, 6)
Simplify function:
F'=A'B'+A'C'+AC
F''=(A'B'+A'C'+AC)'
F=(A+B)(A+C)(A'+C')
3) G(A, B, C) = ∏M (0, 3, 5, 6)
4) H(A, B, C) = ∏M (5, 6)
Simplify the following functions using Karnaugh maps. 1) E(A, B, C) = ∑m (0, 3, 5,...
Use Karnaugh maps to simplify the following Boolean functions ex minterms 1. a) fx,y,z)-ml +m2+ m5+m6+ m7 xy b) f(w, x y,z) -2(0,2,4,5,6,7,12,13) c) f(w, x, y, z) Σ(3, 4, 5, 6, 7, 9, 12, 13, 14, 15) wx
4. Consider these two functions: f- (a' ab) +(a (bd)y -Exclusive-Or) (a) Write the Karnaugh Maps and using them simplify the two functions (b) Algebraically manipulate function f, so that you obtain the same result. (Don't do it for function h.) 4. Consider these two functions: f- (a' ab) +(a (bd)y -Exclusive-Or) (a) Write the Karnaugh Maps and using them simplify the two functions (b) Algebraically manipulate function f, so that you obtain the same result. (Don't do it for...
Using Karnaugh maps, find a minimal sum-of-products expression for each of the following logic functions. F_a = sigma_w, x, y, z(0, 1, 3, 5, 14) + d(8, 15) F_b = sigma_w, x, y, z(0, 1, 2, 8, 11) + d(3, 9, 15) F_c = sigma_A, B, C, D (4, 6, 7, 9, 13) + d(12) F_d = sigma_W, X, Y, Z (4, 5, 9, 13, 15) + d{0, 1, 7, 11, 12)
Simplify the following Boolean functions using four-variable maps: F(w, x, y, z) = Σ (1, 4, 5, 6, 12, 14, 15) F(w, x, y, z) = Π (0, 1, 4, 5, 6, 7, 8, 9) AB’C + B’C’D’ + BCD + ACD’ + A’B’C+ A’BC’D (A xor B)’ (C xor D)
1. (12 points) Simplify the following Boolean functions using K-maps to get smallest implementation (in terms of number of inverters and 2-input AND, and OR gates used): a. F(a, b,c,d) b + bcd +ac a b. W(m,n, q,r) = n(0,2,8,11,12,13,14,15) D(1,4,6,9,10) c. Z(a, b,c, d)E(1,5,7,9,10,12,13) d(0,8,15)
Please simplify the following Product of Sums using Boolean algebra and Karnaugh Maps, where *, +, ' are AND, OR, NOT respectively. Please solve explicitly, making each simplification clear in every step. (Answer should be equivalent in both methods) QM(A,B,C,D) = (A'+B'+C'+D')*(A'+B'+C+D')*(A'+B+C'+D')*(A'+B+C'+D)*(A'+B+C+D')*(A'+B+C+D)*(A+B'+C'+D')
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...
1. (15 pts) Simplify the following Boolean functions using K-maps: a. F(x,y,z) = (1,4,5,6,7) b. F(x, y, z) = (xy + xyz + xyz c. F(A,B,C,D) = 20,2,4,5,6,7,8,10,13,15) d. F(A,B,C,D) = A'B'C'D' + AB'C + B'CD' + ABCD' + BC'D e. F(A,B,C,D,E) = (0,1,4,5,16,17,21,25,29) 2. (12 pts) Consider the combinational logic circuit below and answer the following: a. Derive the Boolean expressions for Fi and F2 as functions of A, B, C, and D. b. List the complete truth table...
1. (10%) Simplify the following Boolean functions or expression, using three-variable maps (0,2,4, 5,6 F(x, y,) lal 4 bl F(r, y, z)xy x'yz y
les K-Map.pdf A (1,0231707 KB) Practice-5 variable K-Map.pdf A (1.868 MB) Use Karnaugh maps to design lowest cost circuits for the following functions with NOT, AND and OR gates. To find the lowest cost, it is a good idea to check both the SOP form of the circuit and POS form of the circuit and compare their cost to find the lowest cost circuit. Hint: Use Karnaugh maps for both SOP and Pos forms and then obtain the simplified expression...