In computers, a bit is a single 1 or 0. It's a contraction of "Binary Digit". In money, historically a bit was an eighth of a gold dollar. One way of making change was to cut the gold dollar up into eight wedges, each then worth 12.5 cents. That's why a quarter is called "two bits".
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To calculate the decimal value of a bit string: Number the bits from right to left 0 - n. Starting with a decimal value of 0, add 2^(Number of that digit) for each 1 you see in your bit string. The sum is the decimal equivalent to the binary number.
1.157920892 x 1077 (rounded)
You need to know what the value is. If the number is 67 and a bit then 67.3 If the number is 673 millionths, then 0.000673
Yes. The derivation is a bit hard to do on here, but it can be found in Physical Chemistry: A Molecular Approach by McQuarrie and Simon.