Question

Compute 2A31_{12} * B75_{12} * 88_{12}. Give your answer as a base 12 integer.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compute this, we first need to convert the numbers to base 10:

2A31_{12} = 2*12^3 + 10*12^2 + 3*12^1 + 1*12^0 = 3517
B75_{12} = 11*12^2 + 7*12^1 + 5*12^0 = 1755
88_{12} = 8*12^1 + 8*12^0 = 104

Now, we multiply these three numbers together:

3517 * 1755 * 104 = 12,328,460

Converting this product back to base 12:

12,328,460 / 12^5 = 3 remainder 6094
6094 / 12^4 = 1 remainder 5574
5574 / 12^3 = 1 remainder 1398
1398 / 12^2 = 1 remainder 42
42 / 12^1 = 3 remainder 6
6 / 12^0 = 6

Therefore, the final answer in base 12 is 3611356.

Answer 2

I get 1BB53AA34

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake in my calculation. Let's recompute the multiplication:

2A31_{12} = 2*12^3 + 10*12^2 + 3*12^1 + 1*12^0 = 3537
B75_{12} = 11*12^2 + 7*12^1 + 5*12^0 = 1755
88_{12} = 8*12^1 + 8*12^0 = 104

3537 * 1755 * 104 = 10,810,066

Now, converting this product back to base 12:

10,810,066 / 12^5 = 4 remainder 3046
3046 / 12^4 = 1 remainder 1102
1102 / 12^3 = 2 remainder 166
166 / 12^2 = 0 remainder 166
166 / 12^1 = 0 remainder 166
166 / 12^0 = 10

Therefore, the correct answer in base 12 is 10421146.