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3) Assume that a logic function F(A, B, C, D) to set the home security system...
A logic circuit realizing the function f has four inputs A, B, C, and D. The...
A logic circuit realizing the function f has four inputs A, B, C, and D. The three inputs A, B, and C are the binary representation of the digits 0 through 7 with A being the most-significant bit. The input D is an odd-parity bit, i.e., the value of D is such that A, B, C, and D always contain an odd number of 1’s. (For example, the digit 1 is represented by ABC = 001 and D = 0,...
The following logic function is given as a sum of minterms F(A,B,C,D) = Σ A,B,C,D(0,1,4,5,9,11,13,15) A)...
The following logic function is given as a sum of minterms F(A,B,C,D) = Σ A,B,C,D(0,1,4,5,9,11,13,15) A) Find out SOP for the function. B) List all the input pair(s) where we can observe a timing hazard from the K-map. C) Draw the timing hazard diagram for one of the input pair. Assume ALL gate delays are equal. Identify the timing hazard from the diagram. D) Write the expression of an equivalent logic function in which the timing hazard(s) is/are eliminated.
Design of a home security system: In order for the system to go on (S =...
Design of a home security system: In order for the system to go on (S = 1), the fire detector must go on (F =1) regardless of the values of the other inputs, or when the motion detector (M) is triggered (activated) with either the front door (D) or the window detector (W) or all three together. Consider the following input variables: F (Fire detector), M (Motion detector), D (Front door) and W (Window detector). The output of the security...
About logic diagram, boolean algebra, computer organization Draw the logic diagram for function F as a...
About logic diagram, boolean algebra, computer organization
Draw the logic diagram for function F as a 2‐level AND‐OR
circuit.
Background
F(a,b,c) --> F output 1 if abc is interpreted as 3-bit
unsigned integer is a prime number. Output is 0 for other
numbers.
The Simplified SOP Expression of F = a'b +
ac
F (a, b, c) =
m (2, 3, 5, 7)
Note:
i) complemented inputs (a', b', c') are not available;
ii) Use a fan‐in of 2 only....
4. Implement the function using only NOR gates (20 pts) (A B+C).D Sketch the logic gate...
4. Implement the function using only NOR gates (20 pts) (A B+C).D Sketch the logic gate schematic and verify your circuit by truth table.
The following logic function is given as a sum of minterms F(W,X,Y,Z) = ∑W,X,Y,Z(2,7,10,13,14) + d(5,6,15)...
The following logic function is given as a sum of minterms F(W,X,Y,Z) = ∑W,X,Y,Z(2,7,10,13,14) + d(5,6,15) a) Draw the K-map for the given function F. b) What is the minimized SOP equation? c) Give all input pairs in the form of WXYZ where a transition between them would create a timing hazard. d) Draw the timing diagram showing the hazard for one of the cases. Assume ALL gate delays are equal. e) Provide the expression of an equivalent logic function...
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy...
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
PROBLEM 3 (13 PTS) a) The following circuit has the following logic function: f = $a+sb....
PROBLEM 3 (13 PTS) a) The following circuit has the following logic function: f = $a+sb. ✓ Complete the truth table of the circuit, and sketch the logic circuit (3 pts) 011 b) We can use several instances of the previous circuit to implement different functions. (10 pts) . For example, the following selection of inputs produce the function: g-X1X + Xxx Demonstrate that this is the case. ini in2 i n3 in | in in6in 0 0 x ....
(d) Translate the following statement into predicate logic: “Every function f :R → R can be...
(d) Translate the following statement into predicate logic: “Every function f :R → R can be written as the sum of an even function and an odd function.” You can use the notation fi + f2 to represent the sum of functions fı and f2, and the notation f1 = f2 to represent the fact that fi and f2 are equal. 2n izo (e) Let n € N, and 20, 21, ..., Q2n E R. Let f: R + R...
A digital logic circuit realizing the function F that has four inputs A, B, C, and...
A digital logic circuit realizing the function F that has four inputs A, B, C, and D. It only accepts inputs in the format: the three inputs A, B, and C are the binary representation of the digits 0 through 7 with A being the MSB and C being the LSB, and the input D has to be an odd-parity bit (i.e., the value of D is such that the number of l’s in the 4 inputs A, B, C,...
Design of a home security system: In order for the system to go on (S = 1), the fire detector must go on (F =1) regardless of the values of the other inputs, or when the motion detector (M) is triggered (activated) with either the front door (D) or the window detector (W) or all three together. Consider the following input variables: F (Fire detector), M (Motion detector), D (Front door) and W (Window detector). The output of the security...
About logic diagram, boolean algebra, computer organization
Draw the logic diagram for function F as a 2‐level AND‐OR
circuit.
Background
F(a,b,c) --> F output 1 if abc is interpreted as 3-bit
unsigned integer is a prime number. Output is 0 for other
numbers.
The Simplified SOP Expression of F = a'b +
ac
F (a, b, c) =
m (2, 3, 5, 7)
Note:
i) complemented inputs (a', b', c') are not available;
ii) Use a fan‐in of 2 only....
4. Implement the function using only NOR gates (20 pts) (A B+C).D Sketch the logic gate schematic and verify your circuit by truth table.
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
PROBLEM 3 (13 PTS) a) The following circuit has the following logic function: f = $a+sb. ✓ Complete the truth table of the circuit, and sketch the logic circuit (3 pts) 011 b) We can use several instances of the previous circuit to implement different functions. (10 pts) . For example, the following selection of inputs produce the function: g-X1X + Xxx Demonstrate that this is the case. ini in2 i n3 in | in in6in 0 0 x ....
(d) Translate the following statement into predicate logic: “Every function f :R → R can be written as the sum of an even function and an odd function.” You can use the notation fi + f2 to represent the sum of functions fı and f2, and the notation f1 = f2 to represent the fact that fi and f2 are equal. 2n izo (e) Let n € N, and 20, 21, ..., Q2n E R. Let f: R + R...
A digital logic circuit realizing the function F that has four inputs A, B, C, and D. It only accepts inputs in the format: the three inputs A, B, and C are the binary representation of the digits 0 through 7 with A being the MSB and C being the LSB, and the input D has to be an odd-parity bit (i.e., the value of D is such that the number of l’s in the 4 inputs A, B, C,...
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