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Algorithms for Integer Arithmetic
Addition Algorithm
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Three Steps to Adding Two Integers
Do they have the same sign? (both positive or both negative) or Do they have opposite signs? (one positive and the other negative)
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Same Signs STEP 2. Enter the common sign: STEP 3.
Now enter the sum of the absolute values: (add the magnitudes)
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Opposite Signs STEP 2. Enter the sign of the number having the larger magnitude: STEP 3. Enter the difference of the larger magnitude and the smaller:
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Work it out!
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Step 1 Same or opposite signs? They have opposite signs.
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Step 2 Enter the sign of the number having the larger magnitude:
|-34| = 34 > 12 = |12|
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Step 3 Subtract the smaller magnitude from the larger and enter the result.
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Work it out!
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Step 1 Same or opposite signs? They have opposite signs.
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Step 2 Enter the sign of the number having the larger magnitude:
|29| = 29 > 14 = |-14|
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Step 3 Subtract the smaller magnitude from the larger and enter the result.
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Work it out!
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Step 1 Same or opposite signs? They are both positive.
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Step 2 The sign is positive.
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Step 3 Add the magnitudes and enter the result.
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Work it out!
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Step 1 Same or opposite signs? They are both negative.
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Step 2 The sign is negative.
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Step 3 Add the magnitudes and enter the result.
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2. Add the two signed numbers:
Adding Many Integers 1. Add all the positive numbers and add all the negative numbers: 2. Add the two signed numbers:
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Work it out! Rigid use of an algorithm is not always best.
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Moral Look before you leap!
Many problems can be worked in your head if you do things in the right order.
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