How do you read binary numbers like 100101001110?

Answer 1

Like base ten, the base two places increase by exponent. The first place is two to the zero power, the second place is two to the first power, the third place is two to the second power and so on. The number you have printed has one 2, one 4, one 8, one 64, one 256 and one 2048

100101001110 base 2 = 2382 base 10

Answer 2

For a number of any base, the digit farthest to the right (if it is a whole number) is worth its value multiplied by the base to the zero power, the next digit to the left is worth the value times the base to the first power, the next digit is worth the value times the base to the second power, and so on. So for binary, which is base 2, the rightmost bit (short for binary digit), which is sometimes called the LSB for Least Significant Bit, is worth 1 x 2^0 if it's a 1 and 0 if it's a zero. Anything raised to the power of zero equals 1. The next bit is worth 2^1 (2) if it's a 1. The next bit is worth 2^2 (4) if it's a 1, and so on. So the number given is

0 x 2^0 +
1 x 2^1 +
1 x 2^2 +
1 x 2^3 +
0 x 2^4 +
0 x 2^5 +
1 x 2^6 +
0 x 2^7 +
1 x 2^8 +
0 x 2^9 +
0 x 2^10 +
1 x 2^11
= 2 + 4 + 8 + 64 + 256 + 2048 = 2382

It helps to have a list of all of the powers of 2 you think you'll need.

Answer 3

100101001110 = 2 + 0 + 0 + 16 + 0 + 64 + 128 + 256 + 0 = 466