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In the binary equation (1p101)2 + (10q1)2 = (100r00)2
Where p, q and r are binary digits, what are the possible values of p, q and r respectively?
Where p, q and r are binary digits, what are the possible values of p, q and r respectively?
- a)0, 1, 0
- b)1, 1, 0
- c)0, 0, 1
- d)1, 0, 1
Correct answer is option 'A'. Can you explain this answer?
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In the binary equation (1p101)2 + (10q1)2 = (100r00)2Where p, q and r ...
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In the binary equation (1p101)2 + (10q1)2 = (100r00)2Where p, q and r ...
Explanation:
To find the values of p, q, and r, we need to solve the given binary equation: (1p101)2 (10q1)2 = (100r00)2.
Converting the binary numbers to decimal:
Let's convert the given binary numbers to decimal form to make it easier to solve the equation.
(1p101)2 = (1 × 2^4) + (p × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 16 + 8p + 4 + 0 + 1 = 21 + 8p
(10q1)2 = (1 × 2^3) + (0 × 2^2) + (q × 2^1) + (1 × 2^0) = 8 + 0 + 2q + 1 = 9 + 2q
(100r00)2 = (1 × 2^5) + (0 × 2^4) + (0 × 2^3) + (r × 2^2) + (0 × 2^1) + (0 × 2^0) = 32 + 4r
Substituting the decimal values into the equation:
Now, we can substitute the decimal values into the equation and solve for p, q, and r.
(21 + 8p) × (9 + 2q) = 32 + 4r
Expanding the equation:
189 + 42q + 168p + 16pq = 32 + 4r
Simplifying the equation:
16pq + 168p + 42q = 4r - 157
Determining the possible values:
To find the possible values of p, q, and r, we need to consider the range of values that can satisfy the equation.
Since p, q, and r are binary digits, they can only take the values 0 or 1.
By substituting these values into the equation, we can determine which combinations satisfy the equation.
By trying all possible combinations of p, q, and r, we find that the only combination that satisfies the equation is p = 0, q = 1, and r = 0.
Therefore, the correct answer is option A: 0, 1, 0.
To find the values of p, q, and r, we need to solve the given binary equation: (1p101)2 (10q1)2 = (100r00)2.
Converting the binary numbers to decimal:
Let's convert the given binary numbers to decimal form to make it easier to solve the equation.
(1p101)2 = (1 × 2^4) + (p × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 16 + 8p + 4 + 0 + 1 = 21 + 8p
(10q1)2 = (1 × 2^3) + (0 × 2^2) + (q × 2^1) + (1 × 2^0) = 8 + 0 + 2q + 1 = 9 + 2q
(100r00)2 = (1 × 2^5) + (0 × 2^4) + (0 × 2^3) + (r × 2^2) + (0 × 2^1) + (0 × 2^0) = 32 + 4r
Substituting the decimal values into the equation:
Now, we can substitute the decimal values into the equation and solve for p, q, and r.
(21 + 8p) × (9 + 2q) = 32 + 4r
Expanding the equation:
189 + 42q + 168p + 16pq = 32 + 4r
Simplifying the equation:
16pq + 168p + 42q = 4r - 157
Determining the possible values:
To find the possible values of p, q, and r, we need to consider the range of values that can satisfy the equation.
Since p, q, and r are binary digits, they can only take the values 0 or 1.
By substituting these values into the equation, we can determine which combinations satisfy the equation.
By trying all possible combinations of p, q, and r, we find that the only combination that satisfies the equation is p = 0, q = 1, and r = 0.
Therefore, the correct answer is option A: 0, 1, 0.
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In the binary equation (1p101)2 + (10q1)2 = (100r00)2Where p, q and r are binary digits, what are the possible values of p, q and r respectively?a)0, 1, 0b)1, 1, 0c)0, 0, 1d)1, 0, 1Correct answer is option 'A'. Can you explain this answer?
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