|
[8] Express the following function as a sum of minterms and as a product of maxterms :
?(?, ?, ?, ?) = ?̅? + ?̅? + ??
[9] Express the complement of the following functions in sum‐of‐minterms form :
(a) ?(?, ? , ?, ?) = ∑(2, 4, 7, 10, 12, 14)
(b) ?( ?, ?, ?) = ∏(3, 5, 7)
[10] Convert each of the following to the other canonical form :
(a) ?(?, ?, ?) = ∑(1, 3, 5)
(b) ?(?, ?, ?, ?) = ∏(3, 5, 8, 11)
[11] Convert each of the following expressions into sum of products and product of sums :
(a) ? = (?? + ?)( ? + ?̅?)
(b) ? = ?̅ + ?(? + ?̅)(? + ?̅)
[12] Express the following functions as CSOP and CPOS expressions:
(a) F(x,y,z) = (x + y' + z)(x + z') + yz in terms of x, y, and z
(b) F(w, x, y, z)=xy ̅̅̅(wz+w̅z̅ )(w+xz ̅ ) in terms of w, x, y, and z
[13] Given the following pulse trains for A, B and C, draw the pulse trains for F1 and F2.
|
![Kingdom of Saudi Arabia
Ministry of Education
Taif University,
College of Computers & Information Technology
Digital Logic Design
503221-4
Assignment 2
[1] Consider a Boolean Algebra <B.+..,0,1> Show that
(a) x.y+xz+yz=x.y + x¹.z
(b) (a+b)'(a'+by' = 0
(x+y)(x + y)
(c) xyz + xy + xyz
(d) (A+B) (A + B)
[2] Algebraically simply the following expressions:
(a) F=abc + abc + ab'c +abc' + a'b'c'
(b) F=y(wz wz) + xy
[3] Simplify the following Boolean expressions to a minimum number of literals!
(a) xy + xy
(b)
(a) AC + ABC +
(b) (79+z)+z+ xy +wx
(c) AB(D+CD) + B(A + ACD)
(d) (A+C)(A+C)(A + B + CD)
[5] Find the complement of the following expressions:
[4] Reduce the following Boolean expressions to the indicated number of literals:
AC
(a) xy + xy
(b)(a + c)(a + b)(a + b + c)
(c) z + Z(0w + xy)
(d) (w+yz)(x + Wz)
المملكة العربية السعودية
وزارة التعليم
جامعة الملف
[6] Given F = ab + b(ad + ac) implement it with AND, OR and inver
[7] Implement the Boolean function
F = xy + yz
(a) With AND, OR, and inverter gates
(b) With OR and inverter gates
(c) With AND and inverter gates
(d) With NAND and inverter gates
(e) With NOR and inverter gates
Assignment 2
كلية الحاسبات وتقنية المعلومات
تصميم منطقي رقعي
1444-1443
to three literals.
to three literals.
to one literals.
to four literals.
gates.
Page 1 of 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7443df15-0229-40ea-9231-4a92f0f38187%2F2b1c0415-0015-4a25-8a83-c802c001f107%2Fnzvurfv_processed.jpeg&w=3840&q=75)
![Kingdom of Saudi Arabia
Ministry of Education
Taif University
College of Computers & Information Technology
Digital Logic Design
503221-4
B
A
F₁
Draw the answers here
[8] Express the following function as a sum of minterms and as a product of maxterms:
F(A,B,C,D)= BD + AD + BD
[9] Express the complement of the following functions in sum-of-minterms form:
(a) F(A,B,C,D) = (2,4,7,10,12,14)
(b) F(x, y, z) = (3, 5, 7)
[10] Convert each of the following to the other canonical form:
(a) F(x, y, z)= (1,3,5)
(b) F(A,B,C,D)=(3, 5, 8, 11)
[11] Convert each of the following expressions into sum of products and product of sums :
(a) F = (AB+C)(B+CD)
(b) F = x + x(x + y)(y + 2)
[12] Express the following functions as CSOP and CPOS expressions:
(a) F(x,y,z) = (x+y' + 2) (x + 2) + yz
in terms of x, y, and z
in terms of w, x, y, and z
(b) F(w, x, y, z)=xy(wz+wz)(w+xz)
[13] Given the following pulse trains for A, B and C, draw the pulse trains for F₁ and F₂.
F₂ B
F₁
جامعة المات
A
F₂
THE CITY
1
0
C 0
1 1
0
1
1
1
0
1
1
1
0
0
1
المملكة العربية السعودية
وزارة التعليم
جـامعة الطائف
0
كلية الحاسبات وتقنية المعلومات
تصميم منطقي رقمي
1
1
1444-1443
1
I
0 1
0
0
1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7443df15-0229-40ea-9231-4a92f0f38187%2F2b1c0415-0015-4a25-8a83-c802c001f107%2F063h7os_processed.jpeg&w=3840&q=75)
