SOLUTION: Write the first fifteen counting numerals for each of the bases below. A. Four B. Eight

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Question 1160767: Write the first fifteen counting numerals for each of the bases below.
A. Four
B. Eight
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

Part A

Counting in base 4 starts off normally (1,2,3) but once we get to 4, we bump up to 10. This is because the digit '4' does not exist in base 4. So we reset back to 0 and add a 1 to the left. Effectively "10" represents 4 in base 4. We say . The subscript tells us which base we're working in.

After 10, we increment like normal (10,11,12,13), then we go from 13 to 20 using the same idea as expressed in the prior paragraph. Think of 13+1 as 10+3+1 = 10+10 = 20. Focus on the 3+1 = 10 portion. This might be confusing if you aren't familiar with base 4 arithmetic, so I recommend getting lots of practice.

Here's the full table showing values in base 10 with corresponding values in base 4

Number in base 10 Number in base 4
1 1
2 2
3 3
4 10
5 11
6 12
7 13
8 20
9 21
10 22
11 23
12 30
13 31
14 32
15 33

Here's a handy calculator to help check your work
https://www.rapidtables.com/convert/number/base-converter.html

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Part B

The same idea applies in base 8. We will count like such,
1,2,3,4,5,6,7,10,11,...
note how 7+1 = 10, because the single digit '8' does not exist in base 8.

Here's what the table would look like

Number in base 10 Number in base 8
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 10
9 11
10 12
11 13
12 14
13 15
14 16
15 17