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Answer:

The positive integer: 0000 0110     ( 610 )

Reflect each bit:     1111 1001

Add one:              1111 1010     ( -610 )

The result is the same representation for minus six as we figured out before.


Negative Six Again

Here is what is going on: When each bit of a pattern is reflected then the two patterns added together make all 1's. This works for all patterns:

      0110 1010   pattern
      1001 0101   pattern reflected
      1111 1111   all columns filled

Adding one to this pattern creates a pattern of all zero's:

     11111 111    row of carry bits
      1111 1111   all columns filled
      0000 0001   one
      0000 0000

The negation algorithm makes use of the above trick. Three patterns added together result in a zero. If one pattern represents an integer, then the sum of the other two patterns represents the negative of the integer.

pattern +  pattern reflected               = all ones

pattern +  pattern reflected + one         = all zeros

pattern + (pattern reflected + one )       = all zeros

pattern + (two's complement of pattern)    = all zeros

Don't be too upset if the above is confusing. Mostly all you need is to get used to this stuff. Of course, this takes practice.


QUESTION 18:

What is the two's complement of 0100 0111?

Reflect:

Add one:


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