Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Two 5-bit binary numbers, i.e. X = 01110 and...
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Two 5-bit binary numbers, i.e. X = 01110 and Y = 11001 are represented in two's complement format. The sum of X and Y represented in two's complement format using 6 bits is
(Answer up to the nearest integer)
Correct answer is '000111'. Can you explain this answer?
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Most Upvoted Answer
Two 5-bit binary numbers, i.e. X = 01110 and Y = 11001 are represente...
Explanation:
Step 1: Convert X and Y to decimal
X = 01110 = -(2^4) + (2^2) + (2^1) = -8 + 4 + 2 = -2
Y = 11001 = -(2^4) + (2^3) + (2^0) = -8 + 8 + 1 = 1
Step 2: Add X and Y
X + Y = -2 + 1 = -1
Step 3: Convert the result to binary
To represent -1 in two's complement format using 6 bits, we need to start with the binary representation of 1, which is 000001. Then we flip all the bits to get 111110, and add 1 to get the final result:
111110 + 000001 = 111111
So the sum of X and Y represented in two's complement format using 6 bits is 111111.
Step 4: Round to the nearest integer
The question asks us to round to the nearest integer, so we need to look at the 6th bit (the leftmost bit) of the binary representation. If it's 0, we round down, and if it's 1, we round up. In this case, the 6th bit is 1, so we round up to get:
111111 rounds up to 000000.
Therefore, the answer is '000000' (rounded up from 111111).
Step 1: Convert X and Y to decimal
X = 01110 = -(2^4) + (2^2) + (2^1) = -8 + 4 + 2 = -2
Y = 11001 = -(2^4) + (2^3) + (2^0) = -8 + 8 + 1 = 1
Step 2: Add X and Y
X + Y = -2 + 1 = -1
Step 3: Convert the result to binary
To represent -1 in two's complement format using 6 bits, we need to start with the binary representation of 1, which is 000001. Then we flip all the bits to get 111110, and add 1 to get the final result:
111110 + 000001 = 111111
So the sum of X and Y represented in two's complement format using 6 bits is 111111.
Step 4: Round to the nearest integer
The question asks us to round to the nearest integer, so we need to look at the 6th bit (the leftmost bit) of the binary representation. If it's 0, we round down, and if it's 1, we round up. In this case, the 6th bit is 1, so we round up to get:
111111 rounds up to 000000.
Therefore, the answer is '000000' (rounded up from 111111).
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Community Answer
Two 5-bit binary numbers, i.e. X = 01110 and Y = 11001 are represente...
MSB of Y is 1, thus it is negative number and X is positive number
Now we have X = 01110 = (14)10
and Y = 11001 = (-7)10
X + Y = (14) + (-7) = 7
In signed two’s complements from 7 is
(7)10 = 000111
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Two 5-bit binary numbers, i.e. X = 01110 and Y = 11001 are represented in two's complement format. The sum of X and Y represented in two's complement format using 6 bits is(Answer up to the nearest integer)Correct answer is '000111'. Can you explain this answer?
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