IEVref: | 171-07-10 | ID: | |

Language: | en | Status: Standard | |

Term: | decision content | ||

Synonym1: | |||

Synonym2: | |||

Synonym3: | |||

Symbol: | H_{0}D_{a}
| ||

Definition: | logarithm of the number of events in a finite set of n mutually exclusive events
EXAMPLE The decision content of a set of three events is: $\begin{array}{l}{H}_{\text{0}}\text{=}\left(\text{lb3}\right)\text{Sh}\approx \text{1}\text{,585}\text{\hspace{0.17em}}\text{Sh}\\ \text{\hspace{1em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{=}\left(\text{ln3}\right)\text{nat}\approx \text{1}\text{,099}\text{\hspace{0.17em}}\text{nat}\\ \text{\hspace{1em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{=}\left(\text{lg3}\right)\text{Hart}\approx \text{0}\text{,477}\text{\hspace{0.17em}}\text{Hart}\end{array}$ Note 1 to entry: The base of the logarithm determines the unit used. Commonly used units are: shannon (symbol Sh) for logarithms of base 2, natural unit (symbol nat) for logarithms of base e, hartley (symbol Hart) for logarithms of base 10. Conversion table: $\begin{array}{lllll}1\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{0,693}\text{\hspace{0.05em}}\text{nat}\hfill & \approx \hfill & \mathrm{0,301}\text{\hspace{0.05em}}\text{Hart}\hfill \\ 1\text{\hspace{0.05em}}\text{nat}\hfill & \approx \hfill & \mathrm{1,433}\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{0,434}\text{\hspace{0.05em}}\text{Hart}\hfill \\ 1\text{\hspace{0.05em}}\text{Hart}\hfill & \approx \hfill & \mathrm{3,322}\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{2,303}\text{\hspace{0.05em}}\text{nat}\hfill \end{array}$ Note 2 to entry: The decision content is independent of the probabilities of the occurrence of the events. Note 3 to entry: The number of decisions needed to select a specific event out of a finite set of mutually exclusive events equals the smallest integer which is greater than or equal to the decision content when the base of the logarithm is the number of choices on each decision. Note 4 to entry: When the same integer base is used for the same number of events, the decision content equals the maximum entropy. | ||

Publication date: | 2019-03-29 | ||

Source | IEC 80000-13:2008, 13-23, modified – The notes to entry have been added | ||

Replaces: | |||

Internal notes: | |||

CO remarks: | |||

TC/SC remarks: | |||

VT remarks: | |||

Domain1: | |||

Domain2: | |||

Domain3: | |||

Domain4: | |||

Domain5: |

*H*_{0}=log *n*

EXAMPLE The decision content of a set of three events is:

$\begin{array}{l}{H}_{\text{0}}\text{=}\left(\text{lb3}\right)\text{Sh}\approx \text{1}\text{,585}\text{\hspace{0.17em}}\text{Sh}\\ \text{\hspace{1em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{=}\left(\text{ln3}\right)\text{nat}\approx \text{1}\text{,099}\text{\hspace{0.17em}}\text{nat}\\ \text{\hspace{1em}}\text{\hspace{0.17em}}\text{\hspace{0.05em}}\text{=}\left(\text{lg3}\right)\text{Hart}\approx \text{0}\text{,477}\text{\hspace{0.17em}}\text{Hart}\end{array}$

Note 1 to entry: The base of the logarithm determines the unit used. Commonly used units are: shannon (symbol Sh) for logarithms of base 2, natural unit (symbol nat) for logarithms of base e, hartley (symbol Hart) for logarithms of base 10.

Conversion table:

$\begin{array}{lllll}1\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{0,693}\text{\hspace{0.05em}}\text{nat}\hfill & \approx \hfill & \mathrm{0,301}\text{\hspace{0.05em}}\text{Hart}\hfill \\ 1\text{\hspace{0.05em}}\text{nat}\hfill & \approx \hfill & \mathrm{1,433}\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{0,434}\text{\hspace{0.05em}}\text{Hart}\hfill \\ 1\text{\hspace{0.05em}}\text{Hart}\hfill & \approx \hfill & \mathrm{3,322}\text{\hspace{0.05em}}\text{Sh}\hfill & \approx \hfill & \mathrm{2,303}\text{\hspace{0.05em}}\text{nat}\hfill \end{array}$

Note 2 to entry: The decision content is independent of the probabilities of the occurrence of the events.

Note 3 to entry: The number of decisions needed to select a specific event out of a finite set of mutually exclusive events equals the smallest integer which is greater than or equal to the decision content when the base of the logarithm is the number of choices on each decision.

Note 4 to entry: When the same integer base is used for the same number of events, the decision content equals the maximum entropy.