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A number is expressed in binary 2's complement as 10011 decimal equivalent value is
- a)19
- b)13
- c)-19
- d)-13
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A number is expressed in binary 2's complement as 10011 decimal equiva...
Explanation:
The 2's complement representation of a negative number is obtained by inverting all the bits and adding 1 to the least significant bit. To get the decimal equivalent of a number represented in 2's complement, we follow the below steps:
1. If the leftmost bit is 1, then the number is negative. In this case, we need to convert the binary number to its 2's complement form.
2. Invert all the bits of the binary number.
3. Add 1 to the least significant bit of the inverted number.
4. The resulting number is the decimal equivalent of the original binary number.
Solution:
The given binary number is 10011.
The leftmost bit is 1, which indicates that the number is negative.
We need to convert the binary number to its 2's complement form.
Invert all the bits of the binary number: 01100
Add 1 to the least significant bit of the inverted number: 01101
The resulting number is 13 in decimal.
However, since the original number was negative, we need to negate the result.
Therefore, the decimal equivalent of the given binary number is -13.
Hence, the correct option is D.
The 2's complement representation of a negative number is obtained by inverting all the bits and adding 1 to the least significant bit. To get the decimal equivalent of a number represented in 2's complement, we follow the below steps:
1. If the leftmost bit is 1, then the number is negative. In this case, we need to convert the binary number to its 2's complement form.
2. Invert all the bits of the binary number.
3. Add 1 to the least significant bit of the inverted number.
4. The resulting number is the decimal equivalent of the original binary number.
Solution:
The given binary number is 10011.
The leftmost bit is 1, which indicates that the number is negative.
We need to convert the binary number to its 2's complement form.
Invert all the bits of the binary number: 01100
Add 1 to the least significant bit of the inverted number: 01101
The resulting number is 13 in decimal.
However, since the original number was negative, we need to negate the result.
Therefore, the decimal equivalent of the given binary number is -13.
Hence, the correct option is D.
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Community Answer
A number is expressed in binary 2's complement as 10011 decimal equiva...
Rightmost bit 1 represents that number is negative
(If it is 0 then number is positive).Left bits are toggled i.e inversed....so they become 1100.finally add 1. so it becomes 1101.And 1101 is 13.Since it was a negative number so it's -13.
(If it is 0 then number is positive).Left bits are toggled i.e inversed....so they become 1100.finally add 1. so it becomes 1101.And 1101 is 13.Since it was a negative number so it's -13.
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