what is 21 base four minus 12 base four equal?

Question

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Answer 1

21 base 4 - 12 base 4 = 9 base 10 - 6 base 10 = 3 base 10

3 base 10 = 3 base 4.

Answer 2

21 base 4 in decimal = 1 * 4^0 + 2 * 4^1 = 1 + 8 = 9
12 base four in decimal = 2 * 4^0 + 1 * 4^1 = 2 + 4 = 6

Therfore 21 base four minus 12 base four in decimal
= 9 - 6 = 3

Answer 3

There are 2 ways to approach this, do the math in base 4, or convert all base 4 numbers to base 10 numbers, and then convert your answer back to base 4...

reading digits from right to left in base 10:
units: 10^0 = 1
tens: 10^1 = 10
so a two digit number TU in base 10 is equal to T*(10^1) + U*(10^0)
reading digits from right to left in base 4:
units: 4^0 = 1
fours: 4^1 = 4
so a two digit number FU in base 10 is equal to F*(4^1) + U*(4^0)


so if it was 21-12 in base 10:
21
-12
you can't take 2 from 1, 2 is less than 1, so you look at the 2 in the tens place. but that's really 2 tens, so you make it 1 ten, regroup and change a ten to 10 units, and you add them to the 1 to make 11 ones. subtract 2 from 11 and you get 9. now you look in the tens place, and instead of 2 you have 1 (because you took away 1), so you have 1 - 1 which is 0. so your answer would be 09 in base 10.

BUT, your question is really in base 4, so we do the math similarily but using base 4 numbers instead...
21
-12
you can't take 2 from 1, 2 is less than 1, so you look at the 2 in the fours place. but that's really 2 fours, so you make it 1 four, regroup and change a four to 4 units, and you add them to the 1 to make 1-1 ones in base 4 (which is really 4+1=5 base 10). subtract 2 from 5 and you get 3. now you look in the fours place, and instead of 2 you have 1 (because you took away 1), so you have 1 - 1 which is 0. so your answer would be 03 in base 4. so that's subtraction in base 4.

now, if we were to convert 21 and 12 (both base 4) over to base 10:
21 base 4 = 2*(4^1) + 1*(4^0) = 2*4 + 1*1 = 8 + 1 = 9 base 10
12 base 4 = 1*(4^1) + 2*(4^0) = 1*4 + 2*1 = 4 + 2 = 6 base 10
in base 10, 9 - 6 = 3
now convert 3 base 10 -> base 4
3*1 = 3*(4^0) = 3 base 4

yea! our answer of 3 is the same through either method.

Answer 4

Either convert back into base 10

2x4 + 1 =9 minus 1x4 +2 = 6
=
3

or subtract normally but if you 'borrow' remember it's a 4 not a 10

Answer 5

I'm assuming you are using logarithms?
it is log base four 21 / log base four 12

Unless you are talking about the base 4 numbering system?
in which case the answer is 3

Answer 6

4__1

2__1
1__2

0__3

21 base 4 - 12 base 4 = 3 base 4

Check
(9 - 6) base ten = 3 base ten = 3 base four

Answer 7

3

Convert them to decimal if it helps.
21(b4) = 2*4 + 1*1 = 9
12(b4) = 1*4 + 2*1 = 6