Example #1: 3.141592653589793
  Stored in memory as 0100000000001001001000011111101101010100010001000010110100011000
  sign bit:           0
  exponent bits:       10000000000
  mantissa bits:                  1001001000011111101101010100010001000010110100011000
  mantissa with implied `1` bit: 11001001000011111101101010100010001000010110100011000
  raw exponent: 1024
  actual exponent (subtracting 1023 from raw): 1
  mantissa with implied bit: 7074237752028440
  final value formula: sign * (mantissa / b^(p-1)) * b^exponent
  b (aka base) = 2
  p (aka precision) = 53
  final value  = 1 * (7074237752028440 / 2^52) * 2^1
  final value  = 1 * (7074237752028440 / 4503599627370496) * 2
  final value  = 884279719003555/281474976710656
  final value  = 3.141592653589793115997963468544185161590576171875
  final value ~= 3.141592653589793



Example #2: 1.0
  Stored in memory as 0011111111110000000000000000000000000000000000000000000000000000
  sign bit:           0
  exponent bits:       01111111111
  mantissa bits:                  0000000000000000000000000000000000000000000000000000
  mantissa with implied `1` bit: 10000000000000000000000000000000000000000000000000000
  raw exponent: 1023
  actual exponent (subtracting 1023 from raw): 0
  mantissa with implied bit: 4503599627370496
  final value formula: sign * (mantissa / b^(p-1)) * b^exponent
  b (aka base) = 2
  p (aka precision) = 53
  final value  = 1 * (4503599627370496 / 2^52) * 2^0
  final value  = 1 * (4503599627370496 / 4503599627370496) * 1
  final value  = 1
  final value ~= 1.0



Example #3: 0.25
  Stored in memory as 0011111111010000000000000000000000000000000000000000000000000000
  sign bit:           0
  exponent bits:       01111111101
  mantissa bits:                  0000000000000000000000000000000000000000000000000000
  mantissa with implied `1` bit: 10000000000000000000000000000000000000000000000000000
  raw exponent: 1021
  actual exponent (subtracting 1023 from raw): -2
  mantissa with implied bit: 4503599627370496
  final value formula: sign * (mantissa / b^(p-1)) * b^exponent
  b (aka base) = 2
  p (aka precision) = 53
  final value  = 1 * (4503599627370496 / 2^52) * 2^-2
  final value  = 1 * (4503599627370496 / 4503599627370496) * 1/4
  final value  = 1/4
  final value  = 0.25



Example #4: 123.456
  Stored in memory as 0100000001011110110111010010111100011010100111111011111001110111
  sign bit:           0
  exponent bits:       10000000101
  mantissa bits:                  1110110111010010111100011010100111111011111001110111
  mantissa with implied `1` bit: 11110110111010010111100011010100111111011111001110111
  raw exponent: 1029
  actual exponent (subtracting 1023 from raw): 6
  mantissa with implied bit: 8687443681197687
  final value formula: sign * (mantissa / b^(p-1)) * b^exponent
  b (aka base) = 2
  p (aka precision) = 53
  final value  = 1 * (8687443681197687 / 2^52) * 2^6
  final value  = 1 * (8687443681197687 / 4503599627370496) * 64
  final value  = 8687443681197687/70368744177664
  final value  = 123.4560000000000030695446184836328029632568359375
  final value ~= 123.456



Example #5: -777.0
  Stored in memory as 1100000010001000010010000000000000000000000000000000000000000000
  sign bit:           1
  exponent bits:       10000001000
  mantissa bits:                  1000010010000000000000000000000000000000000000000000
  mantissa with implied `1` bit: 11000010010000000000000000000000000000000000000000000
  raw exponent: 1032
  actual exponent (subtracting 1023 from raw): 9
  mantissa with implied bit: 6834564278255616
  final value formula: sign * (mantissa / b^(p-1)) * b^exponent
  b (aka base) = 2
  p (aka precision) = 53
  final value  = -1 * (6834564278255616 / 2^52) * 2^9
  final value  = -1 * (6834564278255616 / 4503599627370496) * 512
  final value  = -777
  final value ~= -777.0