Final answer:
3022 base 4 divided by 3 base 4 is equivalent to dividing 202 base 10 by 3 base 10. After performing the division, the answer in base 10 is 67 with a remainder of 1, which converts back to 103 base 4 with a remainder of 1.
Step-by-step explanation:
We are tasked with dividing two numbers that are given in base 4. The numbers are 30224 and 34. To perform this division, we will convert the numbers to base 10, perform the division, and then, if necessary, convert back to base 4 to provide the answer base 4.
Firstly, let's convert 30224 (base 4) to base 10:
= 2*(4^0) + 2*(4^1) + 0*(4^2) + 3*(4^3)
= 2*1 + 2*4 + 0*16 + 3*64
= 2 + 8 + 0 + 192
= 202 (base 10).
Now, we'll convert 34 (base 4) to base 10, which is simply 3 in base 10 since it's a single digit.
Next, we will perform the division in base 10: 202 (base 10) divided by 3 (base 10) gives us 67 with a remainder of 1.
To represent the result in base 4, we'll convert 67 (base 10) to base 4:
- 67 divided by 4 is 16 with a remainder of 3, so the least significant digit (LSD) is 3.
- 16 divided by 4 is 4 with no remainder, so the next digit is 0.
- 4 divided by 4 is 1 with no remainder, so the next digit is 1.
- Since we have now reached a quotient of 1 which is less than 4, this is the most significant digit (MSD).
Assembling the digits from MSD to LSD, we get 1034.
So, 30224 divided by 34 is equal to 1034 with a remainder of 1 (since we had a remainder of 1 when dividing in base 10).