Anyone know anything about bases? I need to write 2032 base four in expanded notation, and then convert it to base ten...

Question

whpalmer4 · Answer

Sure. Base 4 is just like base 10, if you're missing 6 fingers (with apologies to Tom Lehrer, see http://www.youtube.com/watch?v=wIWaJ0sy03g ). $$2032_4 = 2*4^3 + 0*4^2+ 3*4^1 + 2*4^0$$ Instead of the 1s place, 10s place, 100s place, like we do in base 10, we have the 1s place, the 4s place, the 16s places, and the 64s place. For example, if our number happened to be $1234_4$, to convert it to base 10 we would evaluate $1*64 + 2*16 + 3*4 + 4=112_{10}$ and that's all there is to it!

whpalmer4 · Answer

Remember, any non-zero number raised to the 0 power = 1.  To be perfectly clear, I should have written $1*4^3 + 2*4^2 + 3*4^1 + 4*4^0 = 1*64 + 2*16 + 3*4 + 4*1 = 112_{10}$

anonymous · Answer

Correct answer=142

whpalmer4 · Answer

$$2*64 + 0*16 + 3*4 + 2*1 = 128 + 12 + 2 = 142_{10}\checkmark$$