DC2.2 شرح Sheet2 Boolean Algebra شرح امثلة على الجبر المنطقي (جبر بول)
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5 ماه پیش
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Sheet2 examples on Boolean Algebra
Sheet2 examples on Boolean Algebra
شرح امثلة على الجبر المنطقي (جبر بول)
الفيديو يحتوي على اجابة الاسئلة الاتية :
1- Reduce the following Boolean expressions to the indicated number of literals:
(a) A'C' + ABC + AC' to three literals
(b) (x' y' + z)' + z + xy + wz to three literals
(c) A' B(D' + C'D) + B(A + A'CD) to one literal
(d) (A' + C) (A' + C') (A + B + C'D) to four literals
(e) ABC'D + A'BD + ABCD to two literals
2- Draw logic diagrams of the circuits that implement the original and simplified expressions
in Problem 1.
3- List the truth table of the function:
(a) F = xy + xy' + y'z (b) F = bc + a'c'
4- Implement the Boolean function
F = xy + xy' + y'z
(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
5- Simplify the following Boolean functions T1 and T2 to a minimum number of literals:
A B C T1 T2
0 0 0 1 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 0 1
1 0 1 0 1
1 1 0 0 1
1 1 1 0 1
6- Obtain the truth table of the following functions, and express each function in sum‐of‐minterms and product‐of‐maxterms form:
(a) F = (b + cd)(c + bd) (b) F = (cd + b'c + bd')(b + d)
(c) F = (c' + d)(b + c') (d) F = bd' + acd' + ab'c + a'c'
7- For the Boolean function
F = xy'z + x'y'z + w'xy + wx'y + wxy
(a) Obtain the truth table of F.
(b) Draw the logic diagram, using the original Boolean expression.
(c) Use Boolean algebra to simplify the function to a minimum number of literals.
(d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a).
(e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
8- 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)
9- 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)
10- Write Boolean expressions and construct the truth tables describing the outputs of the
circuits described by the logic diagrams in the Figure shown below
_____________________________
الجبر المنطقي
,جبر بول,
Definition of Boolean Algebra.,
Basic Theorems and Properties of Boolean Algebra.,
Boolean Functions.,Canonical and Standard Forms.,
Other Logic Operations.,
Digital Logic Gates.,
reduction of boolean function,
reduction of boolean expression,
تبسيط المعادلات المنطقية
,تبسيط الدوال المنطقية
#voltuino
#فولتوينو
شرح امثلة على الجبر المنطقي (جبر بول)
الفيديو يحتوي على اجابة الاسئلة الاتية :
1- Reduce the following Boolean expressions to the indicated number of literals:
(a) A'C' + ABC + AC' to three literals
(b) (x' y' + z)' + z + xy + wz to three literals
(c) A' B(D' + C'D) + B(A + A'CD) to one literal
(d) (A' + C) (A' + C') (A + B + C'D) to four literals
(e) ABC'D + A'BD + ABCD to two literals
2- Draw logic diagrams of the circuits that implement the original and simplified expressions
in Problem 1.
3- List the truth table of the function:
(a) F = xy + xy' + y'z (b) F = bc + a'c'
4- Implement the Boolean function
F = xy + xy' + y'z
(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
5- Simplify the following Boolean functions T1 and T2 to a minimum number of literals:
A B C T1 T2
0 0 0 1 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 0 1
1 0 1 0 1
1 1 0 0 1
1 1 1 0 1
6- Obtain the truth table of the following functions, and express each function in sum‐of‐minterms and product‐of‐maxterms form:
(a) F = (b + cd)(c + bd) (b) F = (cd + b'c + bd')(b + d)
(c) F = (c' + d)(b + c') (d) F = bd' + acd' + ab'c + a'c'
7- For the Boolean function
F = xy'z + x'y'z + w'xy + wx'y + wxy
(a) Obtain the truth table of F.
(b) Draw the logic diagram, using the original Boolean expression.
(c) Use Boolean algebra to simplify the function to a minimum number of literals.
(d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a).
(e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part (b).
8- 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)
9- 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)
10- Write Boolean expressions and construct the truth tables describing the outputs of the
circuits described by the logic diagrams in the Figure shown below
_____________________________
الجبر المنطقي
,جبر بول,
Definition of Boolean Algebra.,
Basic Theorems and Properties of Boolean Algebra.,
Boolean Functions.,Canonical and Standard Forms.,
Other Logic Operations.,
Digital Logic Gates.,
reduction of boolean function,
reduction of boolean expression,
تبسيط المعادلات المنطقية
,تبسيط الدوال المنطقية
#voltuino
#فولتوينو
5 ماه پیش
در تاریخ 1403/01/18 منتشر شده
است.
366
بـار بازدید شده