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Family Stories

A potpourri of stories about various family members or events

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Binary Birthday Blast - answer

First, let's try converting a easier binary to number to base ten. Consider 1011. This has four digits. The right most digit contributes the value 1 * 2^0 = 1*1=1. The next digit leftward is also a 1, but we need to increase our power of 2 by 1. So, this 1 represents 1 * 2^1 = 1*2 = 2. The next digit is 0 and this represents 0 * 2^2 = 0*4 = 0. And, finally, the last (or first from the left) digit represents 1 * 2^3 = 1*8 = 8. All together, this is 8 + 0 + 2 + 1 = 11.

A Dutch Letter with candles in it

Now, look at the photo again. First note that there are seven candles. Starting from the right side and working leftward, the powers are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, and 2^6. Since we really only count the ones that are lit (since these represent a 1 and unlit a 0), our sum is 2^6 + 2^2 = 64 + 4 = 68. Does this make some sense?