(b) In the second example of the carry, adding 1 and 1 yields 0 with a carry of 1 to the next

position to the left. In the third (most significant digit) position, 1 and 1 plus the carry of 1 results in a 1

with a carry of 1. In the examples below the carry of 1 is reemphasized:

(3) Multiple addition. When several binary 1's appear in the same column, the rules still apply

but the carries sometime become more complex. Actually, it is easier to use the following as an aid.

When an odd number of 1's is added, the sum is 1; when an even number of 1's is added, the sum is 0.

The total number of breakpoints of the radix are carried to the next position as 1's. The following

examples show this procedure.

(a) In this first addition, there is an even number of 1's, causing a carry of a 1 with a 0

entered in the sum. In the second position, there is an addition of 1 and 1 plus the carry of 1, making the

total odd which gives a 1 in the sum and a carry of 1. In the last position, there is another odd addition;

therefore, a sum of 1 plus a carry of 1.