### David Barksdale

Shared publicly -Why $92,233,720,368,547,800?

In binary that's 101000111101011100001010001111010111000010100011111011000. That's a 20-bit pattern that almost repeats 3 times. If we add three leading zeroes we get a nice even 60 bits and the boundaries of the pattern can be shifted without any trouble, then fix the last 7 bits to fit the pattern we get 92,233,720,368,547,758. Was this the actual sum and it got rounded before being reported by BBC? Maybe Mr. Reynolds had the extra $42 already in his account. What does this 20-bit pattern mean? 10100011110101110000

Let's try IEEE floating point format. In binary scientific notation the number is 2^56 * 1.01000111101011100001010001111010111000010100011111011_2. The mantissa is one bit too long to fit in the double-precision format. If we truncate that bit our new number is 92,233,720,368,547,790 and the binary representation is 0100001101110100011110101110000101000111101011100001010001111101. The exponent doesn't follow the nice pattern we have in the mantissa and no sane person would store monetary values in a lossy format like this, so this looks like a dead-end.

Back to the 20-bit pattern. We could Google search all 20 rotations of this pattern for clues, but the very first search turns up a plausible result. This pattern is the repeating bits of the binary expansion of 1/100 and would appear in the floating point representation. This suggests that somewhere in PayPal's code, one penny turned into $92 quadrillion because a floating point number was interpreted as an integer. If only my bank's software would make the same mistake.

In binary that's 101000111101011100001010001111010111000010100011111011000. That's a 20-bit pattern that almost repeats 3 times. If we add three leading zeroes we get a nice even 60 bits and the boundaries of the pattern can be shifted without any trouble, then fix the last 7 bits to fit the pattern we get 92,233,720,368,547,758. Was this the actual sum and it got rounded before being reported by BBC? Maybe Mr. Reynolds had the extra $42 already in his account. What does this 20-bit pattern mean? 10100011110101110000

Let's try IEEE floating point format. In binary scientific notation the number is 2^56 * 1.01000111101011100001010001111010111000010100011111011_2. The mantissa is one bit too long to fit in the double-precision format. If we truncate that bit our new number is 92,233,720,368,547,790 and the binary representation is 0100001101110100011110101110000101000111101011100001010001111101. The exponent doesn't follow the nice pattern we have in the mantissa and no sane person would store monetary values in a lossy format like this, so this looks like a dead-end.

Back to the 20-bit pattern. We could Google search all 20 rotations of this pattern for clues, but the very first search turns up a plausible result. This pattern is the repeating bits of the binary expansion of 1/100 and would appear in the floating point representation. This suggests that somewhere in PayPal's code, one penny turned into $92 quadrillion because a floating point number was interpreted as an integer. If only my bank's software would make the same mistake.

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