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Every pattern of the 256 patterns has been assigned an integer to represent.

The "Sign Bit"

The algorithm that creates the representation of the negative of an integer works with both positive and negative integers. Start with N and form its two's complement: you get -N. Now complement -N and you get the original N.

0110 1101     reflect   1001 0010     add one   1001 0011

1001 0011     reflect   0110 1100     add one   0110 1101

With N-bit two's comp representation, the high order bit is "0" for positive integers and "1" for negative integers. This is a fortunate result. The high order bit is sometimes called the sign bit. But it is not really a sign (it does not play a separate role from the other bits). It takes part in the "binary addition algorithm" just as any bit.


Does the following four-bit two's complement represent a negative or a positive integer?


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