# 9. Extrinsics

## 9.1. Introduction

An extrinsic is a SCALE encoded array consisting of a version number, signature, and varying data types indicating the resulting Runtime function to be called, including the parameters required for that function to be executed.

## 9.2. Preliminaries

###### Definition 152. Extrinsic

An extrinsic , ${t}{x}$, is a tuple consisting of the extrinsic version, ${T}_{{v}}$ (Definition 153), and the body of the extrinsic, ${T}_{{b}}$.

The value of ${T}_{{b}}$ varies for each version. The current version 4 is described in Section 9.3.1..

###### Definition 153. Extrinsic Version

${T}_{{v}}$ is a 8-bit bitfield and defines the extrinsic version. The required format of an extrinsic body, ${T}_{{b}}$, is dictated by the Runtime. Older or unsupported versions are rejected.

The most significant bit of ${T}_{{v}}$ indicates whether the transaction is **signed** (${1}$) or **unsigned** (${0}$). The remaining 7-bits represent the version number. As an example, for extrinsic format version 4, a signed extrinsic represents ${T}_{{v}}$ as `132`

while an unsigned extrinsic represents it as `4`

.

## 9.3. Extrinsics Body

### 9.3.1. Version 4

Version 4 of the Polkadot extrinsic format is defined as follows:

**where**

${A}_{{i}}$ is the multi-address of the sender defined in Definition 154.

${Sig}$: the signature of the sender (Definition 155).

${E}$: the extra data for the extrinsic (Definition 156).

${M}_{{i}}$: the indicator of the Polkadot module (Definition 157).

${F}_{{i}}{\left({m}\right)}$: the indicator of the function of the Polkadot module (Definition 158).

###### Definition 154. Extrinsic Address

Account Id, ${A}_{{i}}$, is the 32-byte address of the sender of the extrinsic as described in the external SS58 address format.

###### Definition 155. Extrinsic Signature

The signature, ${Sig}$, is a varying data type indicating the used signature type, followed by the signature created by the extrinsic author. The following types are supported:

Signature types vary in size, but each individual type is always fixed-size and therefore does not contain a length prefix. `Ed25519`

and `Sr25519`

signatures are 512-bit while `Ecdsa`

is 520-bit, where the last 8 bits are the recovery ID.

The signature is created by signing payload ${P}$.

**where**

${M}_{{i}}$: the module indicator (Definition 157).

${F}_{{i}}{\left({m}\right)}$: the function indicator of the module (Definition 158).

${E}$: the extra data (Definition 156).

${R}_{{v}}$: a UINT32 containing the specification version (

`spec_version`

) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.${F}_{{v}}$: a UINT32 containing the transaction version (

`transaction_version`

) of the Runtime (Section C.4.1.), which can be updated and is therefore subject to change.${H}_{{h}}{\left({G}\right)}$: a 32-byte array containing the genesis hash.

${H}_{{h}}{\left({B}\right)}$: a 32-byte array containing the hash of the block which starts the mortality period, as described in Definition 159.

###### Definition 156. Extra Data

Extra data, ${E}$, is a tuple containing additional metadata about the extrinsic and the system it is meant to be executed in.

**where**

${T}_{mor}$: contains the SCALE encoded mortality of the extrinsic (Definition 159).

${N}$: a compact integer containing the nonce of the sender. The nonce must be incremented by one for each extrinsic created, otherwise, the Polkadot network will reject the extrinsic.

${P}_{{t}}$: a compact integer containing the transactor pay including tip.

###### Definition 157. Module Indicator

${M}_{{i}}$ is an indicator for the Runtime to which Polkadot *module*, ${m}$, the extrinsic should be forwarded to.

${M}_{{i}}$ is a varying data type pointing to every module exposed to the network.

###### Definition 158. Function Indicator

${F}_{{i}}{\left({m}\right)}$ is a tuple which contains an indicator, ${m}_{{i}}$, for the Runtime to which *function* within the Polkadot *module*, ${m}$, the extrinsic should be forwarded to. This indicator is followed by the concatenated and SCALE encoded parameters of the corresponding function, ${p}{a}{r}{a}{m}{s}$.

The value of ${m}_{{i}}$ varies for each Polkadot module since every module offers different functions. As an example, the `Balances`

module has the following functions:

### 9.3.2. Mortality

###### Definition 159. Extrinsic Mortality

Extrinsic **mortality** is a mechanism which ensures that an extrinsic is only valid within a certain period of the ongoing Polkadot lifetime. Extrinsics can also be immortal, as clarified in Section 9.3.2.2..

The mortality mechanism works with two related values:

${M}_{{{per}}}$: the period of validity in terms of block numbers from the block hash specified as ${H}_{{h}}{\left({B}\right)}$ in the payload (Definition 155). The requirement is ${M}_{{{per}}}\geq{4}$ and ${M}_{{{per}}}$ must be the power of two, such as

`32`

,`64`

,`128`

, etc.${M}_{{{pha}}}$: the phase in the period that this extrinsic’s lifetime begins. This value is calculated with a formula, and validators can use this value in order to determine which block hash is included in the payload. The requirement is ${M}_{{{pha}}}<{M}_{{{per}}}$.

In order to tie a transaction’s lifetime to a certain block (${H}_{{i}}{\left({B}\right)}$) after it was issued, without wasting precious space for block hashes, block numbers are divided into regular periods and the lifetime is instead expressed as a "phase" (${M}_{{{pha}}}$) from these regular boundaries:

${M}_{{{per}}}$ and ${M}_{{{pha}}}$ are then included in the extrinsic, as clarified in Definition 156, in the SCALE encoded form of ${T}_{mor}$ (Section 9.3.2.2.). Polkadot validators can use ${M}_{{{pha}}}$ to figure out the block hash included in the payload, which will therefore result in a valid signature if the extrinsic is within the specified period or an invalid signature if the extrinsic "died".

#### 9.3.2.1. Example

The extrinsic author choses ${M}_{{{per}}}={256}$ at block `10'000`

, resulting with ${M}_{{{pha}}}={16}$. The extrinsic is then valid for blocks ranging from `10'000`

to `10'256`

.

#### 9.3.2.2. Encoding

${T}_{mor}$ refers to the SCALE encoded form of type ${M}_{{{per}}}$ and ${M}_{{{pha}}}$. ${T}_{mor}$ is the size of two bytes if the extrinsic is considered mortal, or simply one bytes with a value equal to zero if the extrinsic is considered immortal.

The SCALE encoded representation of mortality ${T}_{mor}$ deviates from most other types, as it’s specialized to be the smallest possible value, as described in Encode Mortality and Decode Mortality.

If the extrinsic is immortal, specify a single byte with a value equal to zero.

###### Algorithm 25. Encode Mortality

\begin{algorithm} \caption{Encode Mortality} \begin{algorithmic} \Require{$M_{per}, M_{pha}$} \Return $0 \enspace \textbf{if} \enspace \textit{extrinsic is immortal}$ \State \textbf{init} $factor = $\call{Limit}{$M_{per} \gg 12, 1, \phi$} \State \textbf{init} $left = $\call{Limit}{\call{TZ}{$M_{per}$}$ - 1, 1, 15$} \State \textbf{init} $right = \frac{M_{pha}}{factor} \ll 4$ \Return $left|right$ \end{algorithmic} \end{algorithm}

###### Algorithm 26. Decode Mortality

\begin{algorithm} \caption{Decode Mortality} \begin{algorithmic} \Require{$T_{mor}$} \Return $\textit{Immortal} \enspace \textbf{if} \enspace T^{b0}_{mor} = 0$ \State \textbf{init} $enc = T^{b0}_{mor} + (T^{b1}_{mor} \ll 8)$ \State \textbf{init} $M_{per} = 2 \ll (enc\ mod\ (1 \ll 4))$ \State \textbf{init} $factor =$ \call{Limit}{$M_{per} \gg 12, 1, \phi$} \State \textbf{init} $M_{pha} = (enc \gg 4) * factor$ \Return $(M_{per}, M_{pha})$ \end{algorithmic} \end{algorithm}

**where**

${T}^{{{b}{0}}}_{\left\lbrace{mor}\right\rbrace}$: the first byte of ${T}_{mor}$.

${T}^{{{b}{1}}}_{\left\lbrace{mor}\right\rbrace}$: the second byte of ${T}_{mor}$.

Limit(${num}$, ${min}$, ${max}$): Ensures that ${num}$ is between ${min}$ and ${max}$. If ${min}$ or ${max}$ is defined as $\phi$, then there is no requirement for the specified minimum/maximum.

TZ(${num}$): returns the number of trailing zeros in the binary representation of ${num}$. For example, the binary representation of

`40`

is`0010 1000`

, which has three trailing zeros.$\gg$: performs a binary right shift operation.

$\ll$: performs a binary left shift operation.

${\mid}$ : performs a bitwise OR operation.