Atari XL - Page 240

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The Atari XL Handbook
01101001
+00010011
01111100
In the case of binary addition we generate a carry
when adding 1 to 1 (in columns 1 and 2 in our
example).
NEGATIVE BINARY NUMBERS
You might have wondered how the computer can
recognise negative numbers, since it can only tell
the difference between on and off. This is achieved
by a method known as 'two's complement' notation,
which uses one bit of the binary number (the most
significant bit, often labelled bit 7) as a sign bit.
To subtract two numbers in binary, we form the
two's complement of the number to be subtracted,
then add it to the other number.
As an example we'll subtract 50 from 100:
100 01100100
-50 00110010
50 00110010
(the answer we want).
To perform the sum in binary, first we find the
two's complement of 50, by changing all the Osto Is
and all the Is to Os, then adding 1.
50 in binary is:
Change Is to Os:
Adding 1 gives
its two's complement:
00110010
11001101
11001110
Now add this to the binary for 100: