Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > If (2.3)base 4+ (1.2)base 4= (y)base 4, what ...
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If (2.3)base 4 + (1.2)base 4 = (y)base 4, what is the value of y?
- a)1.1
- b)10.1
- c)2.01
- d)3.21
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If (2.3)base 4+ (1.2)base 4= (y)base 4, what is the value of y?a)1.1b)...
Solution:
Given: (2.3)base 4 (1.2)base 4 = (y)base 4
We need to convert the given numbers into base 10 to perform the addition operation.
(2.3)base 4 = 2×4^0 + 3×4^-1 = 2.75
(1.2)base 4 = 1×4^0 + 2×4^-1 = 1.5
Now, we can add the two numbers in base 10.
2.75 + 1.5 = 4.25
We need to convert the result back to base 4.
4 = 1×4^1 + 0×4^0 = (10)base 4
0.25 × 4 = 1.0
So, the final answer is (y)base 4 = (10.1)base 4
Therefore, the correct option is B.
Given: (2.3)base 4 (1.2)base 4 = (y)base 4
We need to convert the given numbers into base 10 to perform the addition operation.
(2.3)base 4 = 2×4^0 + 3×4^-1 = 2.75
(1.2)base 4 = 1×4^0 + 2×4^-1 = 1.5
Now, we can add the two numbers in base 10.
2.75 + 1.5 = 4.25
We need to convert the result back to base 4.
4 = 1×4^1 + 0×4^0 = (10)base 4
0.25 × 4 = 1.0
So, the final answer is (y)base 4 = (10.1)base 4
Therefore, the correct option is B.
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Community Answer
If (2.3)base 4+ (1.2)base 4= (y)base 4, what is the value of y?a)1.1b)...
You can do it in two ways:
By converting base 4 into decimal adding them and than converting them back to base 4.
= (2.3)4 + (1.2)4
Here you can minimize the values as:
You can directly convert it to base 4 now, (no need to divide).
= (10.1)4
Alternate method:
As every number has base 4, adding them both and if we get an overflow we take the values as x mod 4 and extra value as carry.
(2.3)
+(1.2)
10.1
(For decimal values 3 + 2 = 5 and 5 mod 4 = 1 carry = 1)
(For units place 2 + 1 + 1 = 4 and 4 mod 4 = 0 carry = 1)
Hence, the correct option is (B).
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