Simplify the following Boolean functions, using three-variable maps: (a) F(x, y, z) = (0,2,6,7) (b) F(x, y, z) = (0,2,3,4,6) (0,1,2,3,7) (c) (d) F(x, y, z) = F(x, y, z)= Σ(3,5,6,7)
Digital Logic Design
[1] Simplify the following Boolean functions, using three-variable maps:
(a) ?(?, ?, ?) = Σ(0, 2, 6, 7)
(b) ?(?, ?, ? )= Σ( 0, 2, 3, 4, 6)
(c) ?(?, ?, ? )= Σ( 0, 1, 2, 3, 7)
(d) ?(?, ?, ? )= Σ (3, 5, 6, 7)
[2] Simplify the following Boolean functions, using four-variable maps:
(a) ? (?, ?, ?, ?) = Σ (1, 4, 5, 6, 12, 14, 15)
(b) ? (?, ?, ?, ?) = Σ (1, 5, 9, 10, 11, 14, 15)
(c) ? (?, ?, ?, ?) = Σ (1, 4, 5, 6, 7, 8, 9)
(d) ? (?, ?, ?, ?) = Σ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)
[3] Simplify the following expressions to (1) sum-of-products and (2) products-of sums:
(a) ?' ? '+ ?' ?' + ??' + ??
(b) ???' + ??' + ??' + ????
(c) ? + ? + ? ? + ? + ? ? + ? + ? (? + ? + ?)
(d) ???' + ??'? + ???
[4] Using K-map derive the minimum SOP expression for each of the following
functions:
(a) F = ab’c’ + ab’c + abc’ +abc
(b) Q = c' + cd + ac + a'bc'd + abc
[5] F(w,x,y,z) = Σ (2, 3, 6, 8, 11, 12, 14)
(a) Show F on a K-map.
(b) Obtain a minimal sum of products expression for F.
(c) If the minterms: m4, m10, m13 and m15 will never occur determine a new minimal
sum of products expression for F.
[6] Convert the following Boolean function from a sum-of-products form to a
simplified product-of-sums form.
?(?, ?, ?, ?) = (0, 1, 2, 5, 8, 10, 13)
![[1] Simplify the following Boolean functions, using three-variable maps:
(0,2,6,7)
(a) F(x, y, z) =
F(x, y, z) =
(b)
(0,2,3,4,6)
(c) F(x, y, z) =
(0,1,2,3,7)
(d) F(x, y, z)=
Σ(3,5,6,7)
[2] Simplify the following Boolean functions, using four-variable maps:
(a) F (w, x, y, z) = (1,4,5,6, 12, 14, 15)
(b)
F
(A,B,C,D)=E(1, 5, 9, 10, 11, 14, 15)
(1,4,5,6,7,8,9)
(c)
F (w, x, y, z) =
(d) F (A,B,C,D) =
(0, 2, 4, 5, 6, 7, 8, 10, 13, 15)
[3] Simplify the following expressions to (1) sum-of-products and (2) products-of-
sums:
(a)
x2 + y2 + y² + xy
(b) ACD + CD + AB + ABCD
(c)
(A+ C + D)(A + B + D)(Ā+ B+ D)(A + B + C)
(d) ABC + ABD + BCD
[4] Using K-map derive the minimum SOP expression for each of the following
functions:
(a) F= ab'c' + ab'c + abc' +abc
(b)
Q = c² + cd + ac + a'be'd + abc
E (2, 3, 6, 8, 11, 12, 14)
[5] F(w,x,y,z)
(a) Show F on a K-map.
(b) Obtain a minimal sum of products expression for F.
(c) If the minterms: m4, mio, mi3 and mis will never occur determine a new minimal
sum of products expression for F.
[6] Convert the following Boolean function from a sum-of-products form to a
simplified product-of-sums form.
F(w, x, y, z) = (0, 1, 2, 5, 8, 10, 13)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3e79f9d-0f65-4df5-9a6a-e3f0786fcb8c%2Ffa7cbdd8-d5fa-4b04-98e5-d7362026ef1a%2Fp9iit1w_processed.jpeg&w=3840&q=75)
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