Final answer:
The 2's complement of the binary number 1010 0000 is obtained by inverting the bits to get 0101 1111 and adding '1' to the LSB, resulting in 0110 0000.
Step-by-step explanation:
To find the 2's complement representation of the binary number 1010 0000, you need to follow two steps:
Invert all the bits of the number, meaning every '0' becomes '1' and every '1' becomes '0'. For the given number, this would yield 0101 1111.
Add '1' to the least significant bit (LSB) of the inverted number. So, 0101 1111 becomes 0101 1111 + '1' which results in 0110 0000. This is the representation you are searching for.
This method is widely used in computer systems to represent negative numbers because it simplifies the process of binary subtraction—it allows the use of the same hardware for both addition and subtraction.
To find the 2's complement representation of the given negative binary number, which is 1010 0000, follow these steps:
Invert the bits: Flip all the bits, changing 1s to 0s and vice versa.
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Original: 1010 0000
Inverted: 0101 1111
Add 1 to the inverted result: After inverting the bits, add 1 to the result.
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Inverted: 0101 1111
+ 1
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Result: 0110 0000
So, the 2's complement representation of the original negative binary number 1010 0000 is 0110 0000. This 2's complement form is used in computing to represent negative integers. The process involves inversion and addition, and it ensures that arithmetic operations, like addition and subtraction, can be performed using the same hardware for both positive and negative numbers.