It Terns Out
Not all computers store values in binary, otherwise known as base-2. Some actually store values in ternary, otherwise known as base-3, it terns (er, turns) out! Rather than use 0, 1, and 2 as their digits, as you might expect, though, those ternary computers tend to use -1, 0, and +1, otherwise known as "balanced" ternary, ordinarily written more succinctly as −, 0, and +, respectively.
Just as the digits in a binary number, otherwise known as bits, represent multiples of powers of 2, so do the digits in a ternary number, otherwise known as trits, represent multiples of powers of 3. In ternary, the rightmost trit can be said to be in the 1s place (i.e., 30); the second-from-right trit can be said to be in the 3s place (i.e., 31); the third-from-right trit can be said to be in the 9s place (i.e., 32); and so forth.
And so a ternary computer would represent, say, -8 through 8, in decimal, as follows in balanced ternary.
| decimal | balanced ternary | because |
|---|---|---|
-8 |
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-7 |
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-6 |
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-5 |
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-4 |
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-3 |
|
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-2 |
|
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-1 |
|
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0 |
|
|
1 |
|
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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Answer the below in ternary.md.
Questions
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(1 point.) How many bits are required to represent, in binary, the decimal number we know as 8, assuming you don’t need to be able to represent negative numbers as well?
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(1 point.) How many trits are required to represent, in balanced ternary, the decimal number we know as 8?
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(1 point.) How many distinct values can you represent in binary with 2 bits?
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(1 point.) How many distinct values can you represent in balanced ternary with 3 trits?
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(1 point.) What is the largest (i.e., most positive) value, in decimal, that you can represent in balanced ternary with 3 trits?
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(1 point.) What is the smallest (i.e., most negative) value, in decimal, that you can represent in balanced ternary with 3 trits?
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(1 point.) How would a ternary computer represent, in balanced ternary, the decimal number we know as 50?
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(2 points.) If the only physical input to a ternary computer is electricity, how might each of
-,0, and+actually be stored electronically?
Debrief
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Which resources, if any, did you find helpful in answering this problem’s questions?
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About how long, in minutes, did you spend on this problem’s questions?