User:Jono4174
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[edit] Theory
The essence of the D/L method is "resources". Each team is taken to have two "resources" to use to make as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand. At any point in any innings, a team's ability to score more runs depends on the combination of these two resources. Looking at historical scores, there is a very close correspondence between the availability of these resources and a team's final score, a correspondence which D/L exploits.
Using a published table which gives the percentage of these combined resources remaining for any number of overs (or, more accurately, balls) left and wickets lost, the target score can be adjusted up or down to reflect the loss of resources to one or both teams when a match is shortened one or more times. This percentage is then used to calculate a target (sometimes called a "par score") that is usually a fractional number of runs, which is then rounded down. If the second team passes the target then the second team is taken to have won the match; if the match ends when the second team has exactly met (but not passed) the target then the match is taken to be a tie.
[edit] Cases
The most significant bit of the mantissa is determined by the value of exponent. If 0 < exponent < 2e − 1, the most significant bit of the mantissa is 1, and the number is said to be normalized. If exponent is 0, the most significant bit of the mantissa is 0 and the number is said to be de-normalized. Three special cases arise:
- if exponent is 0 and mantissa is 0, the number is ±0 (depending on the sign bit)
- if exponent = 2e − 1 and mantissa is 0, the number is ±infinity (again depending on the sign bit), and
- if exponent = 2e − 1 and mantissa is not 0, the number being represented is not a number (NaN).
±(2128 − 2104) ≈ ±3.4028235×1038
This can be summarized as:
| Type | Exponent | Mantissa | Value |
|---|---|---|---|
| Zero | 0000 0000 | 0000 0000 0000 0000 0000 000 | 0.0 |
| Denormalized number | 0000 0000 | 1000 0000 0000 0000 0000 000 | 5.9×10-39 |
| Large normalized number | 1111 1110 | 1111 1111 1111 1111 1111 111 | 3.4×1038 |
| Small normalized number | 0000 0001 | 0000 0000 0000 0000 0000 000 | 1.18×10-38 |
| Infinity | 1111 1111 | 0000 0000 0000 0000 0000 000 | Infinity |
| NaN | 1111 1111 | 0100 0000 0000 0000 0000 000 | NaN |
