Question on Converting between Base Number Systems

Question on Converting Between Base Numbers

The people of Jupiter use Base 13. Therefore, their numerals are 0,1,2,3,4,5,6,7,8,9,A,B,C.

The people on Saturn use Base 7. Therefore, their numerals are 0,1,2,3,4,5,6.

A person on Jupiter has A906BC Jupits on Jupiter. This same person has 65325406 Jupits in her bank account on Saturn.

Which bank account holds more money and by how much?

Thanks so much, really having trouble here with this and any help would be much appreciated!!!

1 Answer

Jovian bank account: $10 \cdot 13^5 + 9 \cdot 13^4 + 6 \cdot 13^2 + 11 \cdot 13^1 + 12 = 3971148 \text{ Jupits}$

Saturnian bank account: $6 \cdot 7^7 + 5 \cdot 7^6 + 3 \cdot 7^5 + 2 \cdot 7^4 + 5 \cdot 7^3 + 4 \cdot 7^2 + 6 = 5586643 \text{ Jupits}$

The remaining parts should be easy for you.

• Hi, I just want to make sure that I am understanding this correctly: Did you not just convert the first number to a DECIMAL number? (Base 10), and then convert the second number from Jupiter to Saturn numbers (Base 7). I'm not sure comparing Base 10 and Base 7 get me the correct answer. If I'm wrong let me know and if you could please explain why i would appreciate that so much!!!!, I just want to understand this question better. – user277331 Oct 6 '15 at 13:47
• @user277331 Both equations are written in decimal. The first one performs a base13 -> base10 conversion. The second one performs a base7 -> base10 conversion. – Henricus V. Oct 6 '15 at 22:46