Yes, that's how it is done. Assuming the contrary should eventually lead you to some contradiction.
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Since there are 8 bits in between, and they can assume any of the two values (0 or 1), that results in a total of 28 different combinations.
The only number that satisfies this condition is zero. When you subtract zero from any number, you will always end up with the same number. This is because subtraction is the inverse operation of addition, and adding zero to a number does not change its value.
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