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March 23rd, 2014, 11:57 AM   #1
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Some binary and ternary facts


How many weights are needed to weight integral weights from 1 to 100?

We can use seven binary weights
[color=beige]. . [/color]to weigh up to 127 pounds.

To weigh 100 pounds, convert 100 to binary:[color=beige] .[/color]

This means:[color=beige] .[/color]





If we can place weights in both pans of the scale,
[color=beige]. . [/color]we can use five ternary weights:[color=beige] .[/color]
[color=beige]. . [/color]to weigh up to 121 pounds.

To weigh 93 pounds, convert to ternary:[color=beige] .[/color]

This means:[color=beige] .[/color]




It can get a bit tricky.

To weigh 100 pounds, convert to ternary:[color=beige] .[/color]

This means:[color=beige] .[/color]



But we don't have two 9-pound weights . . . What can we do?
Add a 9-pound weight to each side.



Of course, we don't have three 9-pound weights, either.
[color=beige]. . [/color]But we can replace them with a 27-pound weight.

[color=beige] . . [/color]There!


Must we go through this juggling every time? . . . No!

Convert 100 to ternary:[color=beige] .[/color]

If a "2' occurs, replace it with "-1" and add 1 to the digit to the left.





The "minus" means that that weight goes on the "other side".



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March 23rd, 2014, 12:39 PM   #2
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Re: Some binary and ternary facts

https://en.wikipedia.org/wiki/Balanced_ternary
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