Subtraction by Complementation

(b) In the first addition, the number of 1's is even, causing a 0 to be entered with two 1's

being carried. The second position has two 1's and two 1's carried making the addition even, with a 0

entered as the sum and two 1's carried again. In the third position, there is one 1 and two 1's carried,

making the addition odd, with a sum of 1 and a carry of 1. In the fourth position, there is a 1 and 1

carried making the addition even, with a 0 entered for the sum and the carry 1 entered as the MSD.

Remember, in any addition of binary numbers, each time the radix (2) is reached, there is a carry of 1 to

the higher order position. The following examples further illustrate this rule.

(c) In Example 2, the sum in the rightmost binary column is a 1 with a 1 carry; in the next

column to the left, the sum is 0 with a carry; the next column's sum is 1 with a 1 carry.

In the final column, a trick can be applied to keep the carry straight. If the column is divided in half, then

a 1 is written as the sum and two 1's are carried as shown:

0 with 1 carry 1

1

0 with 1 carry 1

1

1 Carry from prior column

The two 1's carried now total 10 which are the final two digits.

c. Subtraction by Complementation. Most computers can only add and must use other shortcuts to

accomplish other arithmetic operations. Subtraction is done by adding the complement. Certain

adjustments are necessary.

(1) Decimal complement. To understand the complement and how it is used in computer

subtraction, you must first fully understand the decimal complement. The 10's complement (true

complement) of a number is that quantity which, when added to a number, will total the next breakpoint

or power of 10.

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