Construct the truth table for the following logical expression: (?? ? ??) ? ??. b) Draw the digital...

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Construct the truth table for the following logical expression: (?? ? ??) ? ??. b) Draw the digital circuit which represents the logical expression: (?? ? ??) ? ??, using only AND, OR, and NOT gates.

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Robert · Accepted Answer

1(a)Elements of A are {1, 3, 5, 7, 9} 
1 = 1 * (2 ^ 0) 
3 = 1 * (2^1) + 1 * (2 ^ 0) 
5 = 1 * (2^ 2) + 0 * (2 ^ 1 ) + 1 * (2^ 1) 
7 = 1 * ( 2^ 2) + 1* ( 2^ 1) + 1 * (2 ^ 0) 
9 = 1* ( 2 ^ 3) + 0 * (2 ^ 1) + 0* ( 2 ^ 1 ) + 1 * (2 ^ 0) 
Combining all the representation of the set in the order 
is 1111011111001 
(b)The given pattern of D is divided into 4 sub parts 
which are from right to left 0, 1000, 111, 01 . Then the 
conversion to decimal system is done and the result is 
D = {1, 7, 8, 0} 
© (1) A U B = {1, 3, 5, 6, 7, 9}. The conversion to binary 
is done  like 1 (a)  . The result after combining the 
binary representation for each of them comes out to 
be 1111011101111001 
(2) A (complement) U C  = { 1,3, 5,6,7, 9} 
Similarly the binary representation becomes 
0101001101000.

Construct the truth table for the following logical expression: (?? ? ??) ? ??. b) Draw the digital circuit which represents the logical expression: (?? ? ??) ? ??, using only AND, OR, and NOT gates....

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