| Feature | Balanced Ternary Floating-Point | IEEE-754 Binary Floating-Point |
|---|---|---|
| Base | 3 | 2 |
| Digits | {-1, 0, +1} (often denoted as T, 0, P) | {0, 1} |
| Sign Representation | Implicitly handled by the digits themselves. | Explicit sign bit (0 for positive, 1 for negative). |
| Exponent Representation | Typically represented in balanced ternary, no bias needed. | Biased representation (exponent value + bias). |
| Mantissa Normalization | Leading non-zero digit (+1 or -1) next to the radix point. | Leading '1' (implicit or explicit depending on the format). |
| Representation of Zero | Naturally represented as all zeros (0.0 * 3^any_exponent). | Requires special handling (all exponent and mantissa bits zero, potentially with a sign bit for -0). |
| Special Values | Fewer special cases needed due to inherent sign representation. | Requires special bit patterns for positive/negative infinity, NaN (Not a Number). |
| Symmetry | Inherently symmetric around zero. | Asymmetric representation due to the sign bit. |
| Normalization Goal | Consistent placement of the first non-zero digit. | Ensuring a leading '1' for maximum precision. |
Why IEEE 754 Doesn't Guarantee Uniqueness for Binary Floating Point Numbers:
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Denormalized Numbers (Subnormals): These numbers, used to represent values very close to zero, break the standard normalization rule (leading '1' bit). This means the same value can sometimes be represented as either a normalized number with a small exponent or a denormalized number with a larger exponent.
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Multiple Ways to Represent Zero: IEEE 754 has both positive zero (+0) and negative zero (-0). While they compare as equal, they have different bit patterns.
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Normalization Ambiguity (though less common): While IEEE 754 strongly encourages normalization, subtle differences in rounding during intermediate calculations could theoretically lead to slightly different but equivalent normalized representations in some edge cases (though well-designed implementations minimize this).