Consider the following logical expressions where A + B denotes A logical OR B, AB denotes...
Consider the following logical expressions where A + B denotes A logical OR B, AB denotes A logical AND B, and ¯ A denotes inverse of A. Derive at least one additive (to be added by logical OR operation) term (excluding obvious 0, 1, A ¯ A or similar) which will not affect the result of the expression. For example, adding (by means of logical OR) term B C D to AB C+ ¯AB D does not change the result, for instance AB C+ ¯AB D ≡ B C D+AB C+ ¯AB D. In this case B C D is such an additive term.
(a) AB C + B C ¯ D
(b) AB C + B C D. Note: B C 6= ¯ B ¯ C
(c) AB D + ¯AC + ¯B C
(d) AB C + B ¯ C
(e) ¯AB C D + ¯ A ¯B D + ¯ A ¯C D + AB D
Hint: consider using either consensus theorem or Karnaugh maps
(a.k.a. K-maps) to solve the problem.
Homework Answers
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Consider the following logical expressions where A + B denotes A
logical OR B, AB denotes...
Consider the following logical expressions where A + B denotes A logical OR B, AB denotes...
Consider the following logical expressions where A + B denotes A logical OR B, AB denotes A logical AND B, and ¯ A denotes inverse of A. Derive at least one additive (to be added by logical OR operation) term (excluding obvious 0, 1, A ¯ A or similar) which will not affect the result of the expression. For example, adding (by means of logical OR) term B C D to AB C+ ¯AB D does not change the result,...
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For each of the following regular expressions, use (11.2.3) to construct an NFA. a. (ab)* b....
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Problem 1: consider the following circuit with 4 inputs A, B, c, D, and 3 outputs...
Problem 1:
consider the following circuit with 4 inputs A, B, c, D, and 3 outputs F, G, H. Each input/output is connected to an input/output port. 3-input OR gate Figure 1 a) Determine the Boolean algebra equations relating each input to each output of the circuit. b) Create the truth tables corresponding to the equations obtained above. There should be one truth table per equation c) Produce the Karnaugh maps corresponding to the truth tables d) Determine simplified Boolean...
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1. Prove the following theorem: AB+A'C+B C = AB+ A'C 2. Implement all four Boolean expressions using three half adders only. D = A BOC E = A'BC + AB'C F = ABC'+(A' +B) C G = ABC 3. Two sensors are mounted on a half-white rotating disk as shown below. Sensor output is 5V for white and OV for dark. Specify the digital element or elements to put in the black box so that the LED is ON for...
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)...
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