this development immediately pertains to binaryKpP, where P ∈ {2..K-1}.^[a]

each finite value in the [nonnegative portion of a] value sequence is a arithmetic composition of three components:

1. a trailing significand (a nonnegative integer in the range [0, 2^P-1])

   • this is a fractional binary value

2. an implicit leading bit {0b0, 0b1}

   • the finite value is subnormal when the implicit bit is 0b0 and the trailing significand is non-zero
   • the finite value is normal when the implicit bit is 1b1, whatever the trailing significand may be.

3. an exponent (stored as a nonnegative integer in the range [0, 2^(K-P)-1])

   • the exponent is biased (all values >= 0)
   • to recover its constructive value, subtract the bias (2^(K-P-1)-1) from the biased value.
   • the exponent acts multiplicatively as 2^exponent

each finite value in the [nonnegative portion of a] value sequence is determined with: value = (2^unbiased_exponent) * (implicit_bit + (trailing_significand_bits / 2^P))

• value = (2^unbiased_exponent) * (implicit_bit) + (2^unbiased_exponent) * (trailing_significand / 2^P))
• value = (2^unbiased_exponent) * (implicit_bit) + ((2^unbiased_exponent)/2^P) * (trailing_significand / 1))
• value = (2^unbiased_exponent) * (implicit_bit) + (2^(unbiased_exponent-P) * trailing_significand)
• subnormal value = (2^unbiased_exponent) * (0b0) + (2^(unbiased_exponent-P) * trailing_significand)
• subnormal value = (2^(unbiased_exponent-P) * trailing_significand)
• subnormal value = (2^(unbiased_exponent_min) * trailing_significand)
• normal value = (2^unbiased_exponent) * (0b1) + (2^(unbiased_exponent-P) * trailing_significand)
• normal value = (2^unbiased_exponent) + (2^(unbiased_exponent-P) * trailing_significand)
• normal_value = (2^unbiased_exponent) + subnormal_value