Explain the value in studying base four, for example, in understanding our decimal sytem.?

Answer 1

Learning to think in different bases, gets you used to thinking of what the positional number system we use means...
123₄ means 3x4⁰ + 2x4¹ +1x4²

Just like 123₁₀ means 3x10⁰ + 2x10¹ + 1x10²

You ever wondered why “carrying” worked in multiplication, addition, and subtraction? Well, work with different bases, and it’ll all become clear.

Also, you’ll find that some bases lend themselves to simplified fractions…
½ base 10 = .5. ½ base 12 = .6
¼ base 10 = .25. ¼ base 12 = .3
1/3 base 10 = .333333…. 1/3 base 12 = .4

Answer 2

Nothing uses base 4 does it? It helps learning another base to re-iterate what you know about base 10. The highest digit in base 10 is 9, the next goes into the next place (the 10's place).

With base 4, the highest digit is 3, the next goes into the 4's place. A base 10 number of "4" is written as "10" in base 4... You have a 1 in the 4's place, and a 0 in the 1's place... A few more examples may help.

The decimal 10 doesn't fit in 2 places in base 4, you'd need a 3rd... 1st place, 4s place, and the 8s place.
I think that'd give us "102", it's 1*8+2*1 (2nd number in the products is the place value)

Ah, Maybe I misunderstood the question, but am I making any progress here? :)

It helps you understand places....

the number 42 is 4*10+2
123 is 1*100+2*10+3

ITS SO GREAT. You can do all the bases once you get a hang of it!

Answer 3

The decimal system came about because we have 10 fingers. If you lost your left arm in a bizzare John Deere accident, and had your right thumb bitten off by a doberman, how would you be able to count if you didn't understand base 4?

Answer 4

If for no other reason than that it forces you to learn how to handle polynomials and to recognize that all number systems (to any base) are equivalent.

Doug