Ok, so I figured out a few problems, now I have more on the check list that I cannot understand. Like 100110011101 base two. WTH?

Question

Ok, so I figured out a few problems, now I have more on the check list that I cannot understand.  Like 100110011101 base two.  WTH?

anonymous · Answer

Think about what our normal number system means

14792 in base ten represents

$$14792 = 1*10^4 + 4*10^3 + 7*10^2 + 9*10^1 + 2*10^0$$

So for base 2
100110011101 represents

$$1*2^{11} + 0*2^{10} + 0*2^9 + 1*2^8 + 1*2^7 + 0*2^6 + 0*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0$$
$$= 2^{11} + 2^8 + 2^7 + 2^4 + 2^3 + 2^2 + 2^0$$
$$= 2048 + 256 + 128 + 16 + 8 + 4 + 1$$
$$= 2461$$

anonymous · Answer

Hrm.. part of the equation got cut off.

anonymous · Answer

100110011101 represents

$$1*2^{11} + 0*2^{10} + 0*2^9 + 1*2^8 + 1*2^7 + 0*2^6 + 0*2^5 $$
$$+ 1*2^4 + 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0$$
$$= 2^{11} + 2^8 + 2^7 + 2^4 + 2^3 + 2^2 + 2^0$$
$$= 2048 + 256 + 128 + 16 + 8 + 4 + 1$$
$$= 2461$$