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The sum of the binary numbers (11011)2 , (10110110)2 and (10011x0y)2 is the binary number (101101101)2 . What are the values of x and y?
- a)x = 1, y = 1
- b)x = 1, y = 0
- c)x = 0, y = 1
- d)x = 0, y = 0
Correct answer is option 'B'. Can you explain this answer?
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The sum of the binary numbers (11011)2 , (10110110)2 and (10011x0y)2 i...
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The sum of the binary numbers (11011)2 , (10110110)2 and (10011x0y)2 i...
The decimal value of 11011 is 27, that of 10110110 is 182 whereas let's say, decimal value of 10011x0y is P. Again, decimal value of 101101101 is 365. Hence, 27+182+P=365. Solving this, we get value of P=156. Converting 156 to its binary form, we get 10011100, hence the value of x and y will be 1 and 0 respectively. Hence, option (B) is the correct answer.
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The sum of the binary numbers (11011)2 , (10110110)2 and (10011x0y)2 i...
Explanation:
To solve this problem, we will perform the addition of the given binary numbers step by step.
Step 1:
The sum of the binary numbers (11011)2 and (10110110)2 is calculated by aligning the numbers and adding each corresponding bit.
```
11011
+10110110
----------
```
Starting from the rightmost bit, we add each pair of bits:
- 1 + 0 = 1
- 1 + 1 = 10 (carry over)
- 0 + 1 = 1
- 1 + 1 = 10 (carry over)
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 0 = 1
So, the sum of (11011)2 and (10110110)2 is (110100101)2.
Step 2:
Now, we need to find the value of x and y in the binary number (10011x0y)2.
We know that the sum of the three binary numbers is (101101101)2. So, we can substitute the given binary numbers and solve for x and y.
```
110100101
+ 10011x0y
-----------
101101101
```
Starting from the rightmost bit, we add each pair of bits:
- 1 + y = 1
- 0 + 0 = 0
- 1 + x = 1
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry over)
From the leftmost bit, we have a carry over of 1. Adding the carry over to the next bit:
- 1 + 1 + 1 = 11 (carry over)
Since the leftmost bit is 1, the carry over is 1, and the sum is (101101101)2, we can conclude that x = 1 and y = 0.
Therefore, the correct answer is option B: x = 1, y = 0.
To solve this problem, we will perform the addition of the given binary numbers step by step.
Step 1:
The sum of the binary numbers (11011)2 and (10110110)2 is calculated by aligning the numbers and adding each corresponding bit.
```
11011
+10110110
----------
```
Starting from the rightmost bit, we add each pair of bits:
- 1 + 0 = 1
- 1 + 1 = 10 (carry over)
- 0 + 1 = 1
- 1 + 1 = 10 (carry over)
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 0 = 1
So, the sum of (11011)2 and (10110110)2 is (110100101)2.
Step 2:
Now, we need to find the value of x and y in the binary number (10011x0y)2.
We know that the sum of the three binary numbers is (101101101)2. So, we can substitute the given binary numbers and solve for x and y.
```
110100101
+ 10011x0y
-----------
101101101
```
Starting from the rightmost bit, we add each pair of bits:
- 1 + y = 1
- 0 + 0 = 0
- 1 + x = 1
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry over)
From the leftmost bit, we have a carry over of 1. Adding the carry over to the next bit:
- 1 + 1 + 1 = 11 (carry over)
Since the leftmost bit is 1, the carry over is 1, and the sum is (101101101)2, we can conclude that x = 1 and y = 0.
Therefore, the correct answer is option B: x = 1, y = 0.
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