1-13The sum of each of the first three combinations is obvious:0 + 0 = 0_{2}0 + 1 = 1_{2}1 + 0 = 1_{2}The fourth combination presents a different situation. The sum of 1 and 1 in any other numbersystem is 2, but the numeral 2 does not exist in the binary system. Therefore, the sum of 1_{2} and 1_{2} is 10_{2}(spoken as one zero base two), which is equal to 2_{10}.Study the following examples using the four combinations mentioned above:When a carry is produced, it is noted in the column of the next higher value or in the columnimmediately to the left of the one that produced the carry.Example: Add 1011_{2} and 1101_{2}.Solution: Write out the problem as shown:As we noted previously, the sum of 1 and 1 is 2, which cannot be expressed as a single digit in thebinary system. Therefore, the sum of 1 and 1 produces a carry:

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