# 4 Bit Syntax

### 4.1 Introduction

In Erlang a Bin is used for constructing binaries and matching binary patterns. A Bin is written with the following syntax:

<<E1, E2, ... En>>

A Bin is a low-level sequence of bits or bytes. The purpose of a Bin is to be able to, from a high level, construct a binary,

Bin = <<E1, E2, ... En>>

in which case all elements must be bound, or to match a binary,

<<E1, E2, ... En>> = Bin

where Bin is bound, and where the elements are bound or unbound, as in any match.

In R12B, a Bin need not consist of a whole number of bytes.

A **bitstring** is a sequence of zero or more bits, where
the number of bits doesn't need to be divisible by 8. If the number
of bits is divisible by 8, the bitstring is also a binary.

Each element specifies a certain **segment** of the bitstring.
A segment is a set of contiguous bits of the binary (not
necessarily on a byte boundary). The first element specifies
the initial segment, the second element specifies the following
segment etc.

The following examples illustrate how binaries are constructed or matched, and how elements and tails are specified.

#### Examples

**Example 1: **A binary can be constructed from a set of
constants or a string literal:

Bin11 = <<1, 17, 42>>, Bin12 = <<"abc">>

yields binaries of size 3; binary_to_list(Bin11) evaluates to [1, 17, 42], and binary_to_list(Bin12) evaluates to [97, 98, 99].

**Example 2: **Similarly, a binary can be constructed
from a set of bound variables:

A = 1, B = 17, C = 42, Bin2 = <<A, B, C:16>>

yields a binary of size 4, and binary_to_list(Bin2)
evaluates to [1, 17, 00, 42] too. Here we used a
**size expression** for the variable C in order to
specify a 16-bits segment of Bin2.

**Example 3: **A Bin can also be used for matching: if
D, E, and F are unbound variables, and
Bin2 is bound as in the former example,

<<D:16, E, F/binary>> = Bin2

yields D = 273, E = 00, and F binds to a binary of size 1: binary_to_list(F) = [42].

**Example 4:** The following is a more elaborate example
of matching, where Dgram is bound to the consecutive
bytes of an IP datagram of IP protocol version 4, and where we
want to extract the header and the data of the datagram:

-define(IP_VERSION, 4). -define(IP_MIN_HDR_LEN, 5). DgramSize = byte_size(Dgram), case Dgram of <<?IP_VERSION:4, HLen:4, SrvcType:8, TotLen:16, ID:16, Flgs:3, FragOff:13, TTL:8, Proto:8, HdrChkSum:16, SrcIP:32, DestIP:32, RestDgram/binary>> when HLen>=5, 4*HLen=<DgramSize -> OptsLen = 4*(HLen - ?IP_MIN_HDR_LEN), <<Opts:OptsLen/binary,Data/binary>> = RestDgram, ... end.

Here the segment corresponding to the Opts variable
has a **type modifier** specifying that Opts should
bind to a binary. All other variables have the default type
equal to unsigned integer.

An IP datagram header is of variable length, and its length - measured in the number of 32-bit words - is given in the segment corresponding to HLen, the minimum value of which is 5. It is the segment corresponding to Opts that is variable: if HLen is equal to 5, Opts will be an empty binary.

The tail variables RestDgram and Data bind to binaries, as all tail variables do. Both may bind to empty binaries.

If the first 4-bits segment of Dgram is not equal to 4, or if HLen is less than 5, or if the size of Dgram is less than 4*HLen, the match of Dgram fails.

### 4.2 A Lexical Note

Note that "B=<<1>>" will be interpreted as "B =< <1>>", which is a syntax error. The correct way to write the expression is "B = <<1>>".

### 4.3 Segments

Each segment has the following general syntax:

Value:Size/TypeSpecifierList

Both the Size and the TypeSpecifier or both may be omitted; thus the following variations are allowed:

Value

Value:Size

Value/TypeSpecifierList

Default values will be used for missing specifications. The default values are described in the section Defaults.

Used in binary construction, the Value part is any expression. Used in binary matching, the Value part must be a literal or variable. You can read more about the Value part in the section about constructing binaries and matching binaries.

The Size part of the segment multiplied by the unit in the TypeSpecifierList (described below) gives the number of bits for the segment. In construction, Size is any expression that evaluates to an integer. In matching, Size must be a constant expression or a variable.

The TypeSpecifierList is a list of type specifiers separated by hyphens.

**Type**- The type can be integer, float, or binary.
**Signedness**- The signedness specification can be either signed or unsigned. Note that signedness only matters for matching.
**Endianness**- The endianness specification can be either big, little, or native. Native-endian means that the endian will be resolved at load time to be either big-endian or little-endian, depending on what is "native" for the CPU that the Erlang machine is run on.
**Unit**- The unit size is given as unit:IntegerLiteral. The allowed range is 1-256. It will be multiplied by the Size specifier to give the effective size of the segment. In R12B, the unit size specifies the alignment for binary segments without size (examples will follow).

Example:

X:4/little-signed-integer-unit:8

This element has a total size of 4*8 = 32 bits, and it contains a signed integer in little-endian order.

### 4.4 Defaults

The default type for a segment is integer. The default type does not depend on the value, even if the value is a literal. For instance, the default type in '<<3.14>>' is integer, not float.

The default Size depends on the type. For integer it is 8. For float it is 64. For binary it is all of the binary. In matching, this default value is only valid for the very last element. All other binary elements in matching must have a size specification.

The default unit depends on the the type. For integer, float, and bitstring it is 1. For binary it is 8.

The default signedness is unsigned.

The default endianness is big.

### 4.5 Constructing Binaries and Bitstrings

This section describes the rules for constructing binaries using the bit syntax. Unlike when constructing lists or tuples, the construction of a binary can fail with a badarg exception.

There can be zero or more segments in a binary to be constructed. The expression '<<>>' constructs a zero length binary.

Each segment in a binary can consist of zero or more bits. There are no alignment rules for individual segments of type integer and float. For binaries and bitstrings without size, the unit specifies the alignment. Since the default alignment for the binary type is 8, the size of a binary segment must be a multiple of 8 bits (i.e. only whole bytes). Example:

<<Bin/binary,Bitstring/bitstring>>

The variable Bin must contain a whole number of bytes, because the binary type defaults to unit:8. A badarg exception will be generated if Bin would consist of (for instance) 17 bits.

On the other hand, the variable Bitstring may consist of any number of bits, for instance 0, 1, 8, 11, 17, 42, and so on, because the default unit for bitstrings is 1.

For clarity, it is recommended not to change the unit size for binaries, but to use binary when you need byte alignment, and bitstring when you need bit alignment.

The following example

<<X:1,Y:6>>

will successfully construct a bitstring of 7 bits. (Provided that all of X and Y are integers.)

As noted earlier, segments have the following general syntax:

Value:Size/TypeSpecifierList

When constructing binaries, Value and Size can be any Erlang expression. However, for syntactical reasons, both Value and Size must be enclosed in parenthesis if the expression consists of anything more than a single literal or variable. The following gives a compiler syntax error:

<<X+1:8>>

This expression must be rewritten to

<<(X+1):8>>

in order to be accepted by the compiler.

#### Including Literal Strings

As syntactic sugar, an literal string may be written instead of a element.

<<"hello">>

which is syntactic sugar for

<<$h,$e,$l,$l,$o>>

### 4.6 Matching Binaries

This section describes the rules for matching binaries using the bit syntax.

There can be zero or more segments in a binary pattern. A binary pattern can occur in every place patterns are allowed, also inside other patterns. Binary patterns cannot be nested.

The pattern '<<>>' matches a zero length binary.

Each segment in a binary can consist of zero or more bits.

A segment of type binary must have a size evenly divisible by 8 (or divisible by the unit size, if the unit size has been changed).

A segment of type bitstring has no restrictions on the size.

As noted earlier, segments have the following general syntax:

Value:Size/TypeSpecifierList

When matching Value value must be either a variable or an integer or floating point literal. Expressions are not allowed.

Size must be an integer literal, or a previously bound variable. Note that the following is not allowed:

foo(N, <<X:N,T/binary>>) -> {X,T}.

The two occurrences of N are not related. The compiler will complain that the N in the size field is unbound.

The correct way to write this example is like this:

foo(N, Bin) -> <<X:N,T/binary>> = Bin, {X,T}.

#### Getting the Rest of the Binary or Bitstring

To match out the rest of a binary, specify a binary field without size:

foo(<<A:8,Rest/binary>>) ->

The size of the tail must be evenly divisible by 8.

To match out the rest of a bitstring, specify a field without size:

foo(<<A:8,Rest/bitstring>>) ->

There is no restriction on the number of bits in the tail.

### 4.7 Appending to a Binary

In R12B, the following function for creating a binary out of a list of triples of integers is now efficient:

triples_to_bin(T) -> triples_to_bin(T, <<>>). triples_to_bin([{X,Y,Z} | T], Acc) -> triples_to_bin(T, <<Acc/binary,X:32,Y:32,Z:32>>); % inefficient before R12B triples_to_bin([], Acc) -> Acc.

In previous releases, this function was highly inefficient, because the binary constructed so far (Acc) was copied in each recursion step. That is no longer the case. See the Efficiency Guide for more information.