Add new notes from 11.10.2024 and earlier

notes/20241014194001.md

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+# How to apply binary operations to numbers as floats?
+To apply any binary operation (an operation, that needs 2 operands) to numbers as floats [[20241010165723]] do the following things:
+1. Normalize the number
+2. Bring the numbers to the same exponent (by shifting the larger number number to the right) (the new bits fill the guard, round and sticky bit [[20241014194612]])
+3. Apply your operation to the mantissas of the numbers
+4. Apply the rules for the GRS bits to the result [[20241014195117]].
+
+#gds #floatingpoint

notes/20241014194612.md

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+# What are the guard, round and sticky bits (GRS)?
+The guard, round and sticky bits are bits, that are appended to floating point numbers [[20241010165723]] in order to allow for maximum accuracy when applying operations. To be precise they have the function of ensuring, that an operation applied to rounded operands returns the same result as the rounded result of 
+the operation with unrounded operands. 
+
+#gds #floatingpoint

notes/20241014195117.md

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+# What are the rules for optimal rounding with the guard, round and sticky bit?
+The rules for optimal rounding of floating point numbers [[20241010165723]] using the guard, round and sticky [[20241014194612]] bit are described in the following table:
+
+| G | R | S | Mantissa                         |
+|---|---|---|----------------------------------|
+| 0 | x | x | Unchanged (round down)           |
+| 1 | 1 | x |  Result += 1 (round up)          |
+| 1 | 0 | 0 | if lsb is 0 unchanged, else  +=1 |
+| 1 | 0 | 1 | Result += 1 (round up)           |
+
+#gds #floatingpoint