Write the binary number 1010101010101010 as a decimal number.
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This is Giancoli Answers with Mr. Dychko. Each binary digit represents a decimal quantity, two to the power of something. So the first digit represents two to the power of zero, If the digit is set. And then the next digit represents two to the power of one if the digit is set and then the next one is two to the power of two and we can see that it's always the place value minus one is gonna be the exponent. So this place value here is place value one and the exponent is zero so that's one minus one makes zero. And this place value is a is three, the third place value. And so we'll call that the n here as its exponent, two to the power of n minus one here. So three minus one makes two. And so on. So we'll extend that pattern here. So we have two to the power of one is set. And so we've written that plus two to the power of the fourth place value which is going to be two power of three. And then we have one, two, three, four, five, six place values. That's two power six minus one, so two to the power of five and seven and eight place values set. So it's two to the power of eight minus one. And so on, and so on, and so on. We get 43690 when you go through that process.
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