# Thread: Need help identifying pros and cons for different base numeric systems

1. ## Need help identifying pros and cons for different base numeric systems

I have to write a paper for my math class about which number system would be the best for a new civilization to adopt. The bases I can choose from are base 2, base 5, and base 6. What are the pros and cons to each of these? I know how to solve problems with bases and what not, but I dunno any pros and cons are to each one. Thanks for any help.

Note: We can't make a decision based off how our anatomy (fingers and toes).

2. Originally Posted by Taclooc
I have to write a paper for my math class about which number system would be the best for a new civilization to adopt. The bases I can choose from are base 2, base 5, and base 6. What are the pros and cons to each of these? I know how to solve problems with bases and what not, but I dunno any pros and cons are to each one. Thanks for any help.

Note: We can't make a decision based off how our anatomy (fingers and toes).
If computers are considered, it is not very hard to show why base 2 makes sense in that context. I'm afraid the notion of new civilization adopting a number system isn't very well defined. In general it can make sense to use one base for one context, and another base for another context. From a programming perspective, the bases you run into most often are 2, 10, and 16.

It does not make much sense to use base 2 on paper, because it takes too long to write out the numbers, and it's hard for the eye to distinguish different numbers at a glance, etc.

3. Originally Posted by undefined
If computers are considered, it is not very hard to show why base 2 makes sense in that context. I'm afraid the notion of new civilization adopting a number system isn't very well defined. In general it can make sense to use one base for one context, and another base for another context. From a programming perspective, the bases you run into most often are 2, 10, and 16.

It does not make much sense to use base 2 on paper, because it takes too long to write out the numbers, and it's hard for the eye to distinguish different numbers at a glance, etc.
It's a really dumb assignment. The description basically says "You are Zirkle from the planet Zordon (power rangers much?) and you are preparing recommendations for a number system to adopt for your planet. You have examined three different bases; base-5, base-2, and base-6. Summarize the pros and cons of each base and tell which base you recommend for your planet to adopt."

4. Originally Posted by Taclooc
It's a really dumb assignment. The description basically says "You are Zirkle from the planet Zordon (power rangers much?) and you are preparing recommendations for a number system to adopt for your planet. You have examined three different bases; base-5, base-2, and base-6. Summarize the pros and cons of each base and tell which base you recommend for your planet to adopt."
Haha, just make general statements then, like how with a larger base number system you can write larger numbers with fewer symbols, etc.

(The sentence I just wrote might have been hard to follow.. what I mean is that, for example, the number 10000 in base 10 requires 5 symbols, but in base 16 it is 2710 hence requires only 4 symbols; in base 2 it requires 14 symbols.)

5. Appreciate the help, man.

6. Hello, Taclooc!

I have to write a paper for my math class about which number system
would be the best for a new civilization to adopt.
The bases I can choose from are base 2, base 5, and base 6.
What are the pros and cons to each of these?

We probably use a base-10 system because we have
. . ten digits (fingers and thumbs) on our hands.

Using both hands, we can represent any integer from 0 to 10
. . by holding up the appropriate number of fingers.

. . For example: . $\begin{array}{ccc}\;\;\backslash\:|\:/ & \!\!\backslash\:|\;/ \\[-1mm] -\! \bigcirc\!\_ & \_\bigcirc- \end{array}$ . represents "ten".

For numbers greater than 10, we must "flash" both hands, then the final digit.

. . For example: .23 would be: . $\text{("flash")}\quad \text{("flash")} \quad \begin{array}{c} \backslash | / \\[-1mm] \bigcirc \end{array}$

For numbers greater than 99, this system is impractical.

A civilization with a base-two system would be more efficient.

An extended finger represents "1" and a bent (hidden) finger represents "0".

I will use "o" to represent a hidden finger.

Then: . $\begin{array}{cc}\; _o\, |\, _o & \!\!\backslash\, _o\, / \\ - \bigcirc\,\! _o & _o\bigcirc - \end{array}$ . represents $1,\!010,\!001,\!011_2 \;=\;651$

With ten fingers and a base-2 system, we can represent numbers up to 1023.

A base-3 system can be counted on our ten fingers up to 59,048
. . I'll let you work out the details.

7. Originally Posted by Soroban

Then: . $\begin{array}{cc}\; _o\, |\, _o & \!\!\backslash\, _o\, / \\ - \bigcirc\,\! _o & _o\bigcirc - \end{array}$ . represents $1,\!010,\!001,\!011_2 \;=\;651$
This is neat, although practically speaking it is rather hard to contort one's hand for arbitrary finger positions.

Originally Posted by Soroban

A base-3 system can be counted on our ten fingers up to 59,048
. . I'll let you work out the details.
I suppose it is something along the lines of allowing a finger to be hidden, fully extended, or curled?

Originally Posted by Soroban

For numbers greater than 10, we must "flash" both hands, then the final digit.
Here's another option. Use your right hand to indicate numbers from 0-9 as follows: palm forward gives 0-5, and the reverse gives 6-9 (actually we have two leftover we could use as 10 and 11, perfect for base 12)

Do the same with the left hand. Then we can easily represent any number up to 99 without any flashing, plus we could use base 100 to get higher numbers with flashing. Or we could allow the left hand and right hand to cross, giving us more options. Or we could orient a hand pointing up, left, right, or down for more options.

Edit: Or we could just represent 23 by flashing 2 then 3. This seems a bit simpler haha.

8. Originally Posted by Taclooc
I have to write a paper for my math class about which number system would be the best for a new civilization to adopt. The bases I can choose from are base 2, base 5, and base 6. What are the pros and cons to each of these? I know how to solve problems with bases and what not, but I dunno any pros and cons are to each one. Thanks for any help.

Note: We can't make a decision based off how our anatomy (fingers and toes).
Imperial measures are sprinkled with binary numbers like 2, 4, 8 and so on, and with the high-factor numbers, like 12. The Babylonians liked 60, a high-factor number, giving us minutes and seconds, and degrees, minutes and seconds.

Binary systems for weights, used in commerce, are useful because they require the minimum number of standard weights 1, 2, 4, 8 etc. Combining them gives you any weight you want.

Others have posted about counting in binary. The science-fiction writer, Frederick Pohl, wrote a short piece called, "How to count on your fingers". See this page, Binary Counting

I find it useful to press the tips of my "1" fingers on the edge of a desk or table.

Pohl suggested we changed to an binary/hex system, using words like "poot" for 1001, "ooty" for 0011, and, of course, "pohl" for 1011. (A consonant is a 1 digit, a vowel is a 0.)

High-factor numbers, of course, can be divided up in a large number of ways, which again, is of practical use. It might be interesting to make a table of numbers and their factors.

Based on the above, I'd choose base 2 or 6 over base 5. My choice would be base 2, "oota";