Faced with the specter of having to memorize addition tables, and with the reward of building a calculator from scratch, our six year old—aka No. 1—and I have been working on math
from a slightly different tack. We switched to base 2 numbers. Base 2 numbers, also known as binary, are the numbers all computers use. For those unfamiliar with binary numbers, the binary system, (technically referred to as a ‘base 2’), only gives you two numbers to work with: 0 and 1. Consequently, the binary addition table is far easier to memorize:
Addition Table
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||
+
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0
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1
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0
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0
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1
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1
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1
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10
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In contrast, the number
system we’re all familiar with, (known as ‘base 10’), gives us 10 numbers to
work with: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Given a single digit in our ‘normal’ base 10 system, we can represent up
to 9 things. If we have ten things, we
have to add a new digit—known as the ten’s place—hence 10 uses two digits. In base 2, given one digit, we can represent
at most one thing. So, when we want to
represent two things, we have to add a new digit—known as the two’s place—so in
the table above, when we add one with one, the result—two—is written as 10 in
base 2.
The concept of ‘carrying’ was easier for us
because we didn’t have to use such large numbers to practice. You might not think adding 4 to 6 is a big deal, but you also might have memorized your addition tables more than a
decade ago.
No. 1 and I discovered that we when needed to carry what had really happened was that we’d run out of room adding two digits together. In other words, when we add two one digit
numbers together, and need to write the answer as a two digit number, we’ve
carried. For normal base 10 numbers, you
‘run out of room’ when you add two numbers and wind up with an answer larger
than 9. In base 2, you carry when you
add two numbers and come up with an answer larger than one. Consequently, we wind up carrying in almost
every math problem. No. 1’s getting all
the benefit of practicing carrying without having to memorize a 100 entry
addition table first.
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