ISO/IEC 8825-1:2021

INTERNATIONAL ISO/IEC
STANDARD 8825-1
Sixth edition
2021-06
Information technology — ASN.1
encoding rules —
Part 1:
Specification of Basic Encoding Rules
(BER), Canonical Encoding Rules
(CER) and Distinguished Encoding
Rules (DER)
Technologies de l'information — Règles de codage ASN.1 —
Partie 1: Spécification des règles de codage de base (BER), des règles
de codage canoniques (CER) et des règles de codage distinctives
(DER)
Reference number
©
ISO/IEC 2021
© ISO/IEC 2021
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ii © ISO/IEC 2021 – All rights reserved

Foreword
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This document was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 6, Telecommunications and information exchange between systems, in collaboration
with ITU-T. The identical text is published as ITU-T X.690 (02/2021).
This sixth edition cancels and replaces the fifth edition (ISO/IEC 8825-1:2015), which has been
technically revised.
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© ISO/IEC 2021 – All rights reserved iii

CONTENTS
Page
Introduction . v
1 Scope . 1
2 Normative references . 1
2.1 Identical Recommendations | International Standards. 1
2.2 Additional references . 1
3 Definitions . 2
4 Abbreviations . 2
5 Notation . 3
6 Convention . 3
7 Conformance . 3
8 Basic encoding rules . 3
8.1 General rules for encoding . 3
8.1.1 Structure of an encoding . 3
8.1.2 Identifier octets . 4
8.1.3 Length octets . 5
8.1.4 Contents octets . 6
8.1.5 End-of-contents octets . 6
8.2 Encoding of a boolean value . 7
8.3 Encoding of an integer value. 7
8.4 Encoding of an enumerated value . 7
8.5 Encoding of a real value . 7
8.6 Encoding of a bitstring value . 9
8.7 Encoding of an octetstring value . 10
8.8 Encoding of a null value . 10
8.9 Encoding of a sequence value . 10
8.10 Encoding of a sequence-of value . 11
8.11 Encoding of a set value . 11
8.12 Encoding of a set-of value . 11
8.13 Encoding of a choice value . 11
8.14 Encoding of a value of a prefixed type . 11
8.15 Encoding of an open type . 12
8.16 Encoding of an instance-of value . 12
8.17 Encoding of a value of the embedded-pdv type . 13
8.18 Encoding of a value of the external type . 13
8.19 Encoding of an object identifier value . 14
8.20 Encoding of a relative object identifier value . 15
8.21 Encoding of an OID internationalized resource identifier value. 15
8.22 Encoding of a relative OID internationalized resource identifier value . 15
8.23 Encoding for values of the restricted character string types . 15
8.24 Encoding for values of the unrestricted character string type . 18
8.25 Encoding for values of the Useful Types . 18
8.26 Encoding for values of the TIME type and the useful time types . 18
8.26.1 Encoding for values of the TIME type . 18
8.26.2 Encoding for values of the DATE type . 18
8.26.3 Encoding for values of the TIME-OF-DAY type . 18
8.26.4 Encoding for values of the DATE-TIME type . 18
8.26.5 Encoding for values of the DURATION type . 18
Rec. ITU-T X.690 (02/2021) iii
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9 Canonical encoding rules . 19
9.1 Length forms . 19
9.2 String encoding forms . 19
9.3 Set components. 19
10 Distinguished encoding rules . 19
10.1 Length forms . 19
10.2 String encoding forms . 20
10.3 Set components. 20
11 Restrictions on BER employed by both CER and DER . 20
11.1 Boolean values . 20
11.2 Unused bits . 20
11.3 Real values . 20
11.4 GeneralString values . 21
11.5 Set and sequence components with default value . 21
11.6 Set-of components . 21
11.7 GeneralizedTime . 21
11.8 UTCTime . 21
11.8.4 Examples of valid representations . 22
11.8.5 Examples of invalid representations . 22
11.9 The TIME type and the useful time types . 22
12 Use of BER, CER and DER in transfer syntax definition . 22
Annex A – Example of encodings. 24
A.1 ASN.1 description of the record structure . 24
A.2 ASN.1 description of a record value . 24
A.3 Representation of this record value . 24
Annex B – Identification of Encoding Rules . 26
Annex C – Illustration of real value encoding . 27
iv Rec. ITU-T X.690 (02/2021)
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Introduction
Rec. ITU-T X.680 | ISO/IEC 8824-1, Rec. ITU-T X.681 | ISO/IEC 8824-2, Rec. ITU-T X.682 | ISO/IEC 8824-3, Rec.
ITU-T X.683 | ISO/IEC 8824-4 (Abstract Syntax Notation One or ASN.1) together specify a notation for the definition
of abstract syntaxes, enabling application standards to define the types of information they need to transfer. It also
specifies a notation for the specification of values of a defined type.
This Recommendation | International Standard defines encoding rules that may be applied to values of types defined using
the ASN.1 notation. Application of these encoding rules produces a transfer syntax for such values. It is implicit in the
specification of these encoding rules that they are also to be used for decoding.
There may be more than one set of encoding rules that can be applied to values of types that are defined using the ASN.1
notation. This Recommendation | International Standard defines three sets of encoding rules, called basic encoding rules,
canonical encoding rules and distinguished encoding rules. Whereas the basic encoding rules give the sender of an
encoding various choices as to how data values may be encoded, the canonical and distinguished encoding rules select
just one encoding from those allowed by the basic encoding rules, eliminating all of the sender's options. The canonical
and distinguished encoding rules differ from each other in the set of restrictions that they place on the basic encoding
rules.
The distinguished encoding rules is more suitable than the canonical encoding rules if the encoded value is small enough
to fit into the available memory and there is a need to rapidly skip over some nested values. The canonical encoding rules
is more suitable than the distinguished encoding rules if there is a need to encode values that are so large that they cannot
readily fit into the available memory or it is necessary to encode and transmit a part of a value before the entire value is
available. The basic encoding rules is more suitable than the canonical or distinguished encoding rules if the encoding
contains a set value or set-of value and there is no need for the restrictions that the canonical and distinguished encoding
rules impose. This is due to the memory and CPU overhead that the latter encoding rules exact in order to guarantee that
set values and set-of values have just one possible encoding.
Annex A gives an example of the application of the basic encoding rules. It does not form an integral part of this
Recommendation | International Standard.
Annex B summarizes the assignment of object identifier and OID internationalized resource identifier values made in this
Recommendation | International Standard. It does not form an integral part of this Recommendation | International
Standard.
Annex C gives examples of applying the basic encoding rules for encoding reals. It does not form an integral part of this
Recommendation | International Standard.

Rec. ITU-T X.690 (02/2021) v
© ISO/IEC 2021 – All rights reserved

INTERNATIONAL STANDARD
ITU-T RECOMMENDATION
Information technology – ASN.1 encoding rules:
Specification of Basic Encoding Rules (BER),
Canonical Encoding Rules (CER)
and Distinguished Encoding Rules (DER)
1 Scope
This Recommendation | International Standard specifies a set of basic encoding rules that may be used to derive the
specification of a transfer syntax for values of types defined using the notation specified in Rec. ITU-T X.680 |
ISO/IEC 8824-1, Rec. ITU-T X.681 | ISO/IEC 8824-2, Rec. ITU-T X.682 | ISO/IEC 8824-3, and Rec. ITU-T X.683 |
ISO/IEC 8824-4, collectively referred to as Abstract Syntax Notation One or ASN.1. These basic encoding rules are also to
be applied for decoding such a transfer syntax in order to identify the data values being transferred. It also specifies a set of
canonical and distinguished encoding rules that restrict the encoding of values to just one of the alternatives provided by the
basic encoding rules.
2 Normative references
The following Recommendations and International Standards contain provisions which, through reference in this text,
constitute provisions of this Recommendation | International Standard. At the time of publication, the editions indicated were
valid. All Recommendations and Standards are subject to revision, and parties to agreements based on this Recommendation
| International Standard are encouraged to investigate the possibility of applying the most recent edition of the
Recommendations and Standards listed below. Members of IEC and ISO maintain registers of currently valid International
Standards. The Telecommunication Standardization Bureau of the ITU maintains a list of currently valid ITU-T
Recommendations.
NOTE – This Recommendation | International Standard is based on ISO/IEC 10646:2003. It cannot be applied using later versions of
this standard.
2.1 Identical Recommendations | International Standards
– Recommendation ITU-T X.200 (1994) | ISO/IEC 7498-1: 1994, Information technology – Open Systems
Interconnection – Basic Reference Model: The basic model.
– Recommendation ITU-T X.680 (2021) | ISO/IEC 8824-1:2021, Information technology – Abstract Syntax
Notation One (ASN.1): Specification of basic notation.
– Recommendation ITU-T X.681 (2021) | ISO/IEC 8824-2:2021, Information technology – Abstract Syntax
Notation One (ASN.1): Information object specification.
– Recommendation ITU-T X.682 (2021) | ISO/IEC 8824-3:2021, Information technology – Abstract Syntax
Notation One (ASN.1): Constraint specification.
– Recommendation ITU-T X.683 (2021) | ISO/IEC 8824-4:2021, Information technology – Abstract Syntax
Notation One (ASN.1): Parameterization of ASN.1 specifications.
NOTE – The references above shall be interpreted as references to the identified Recommendations | International Standards together
with all their published amendments and technical corrigenda.
2.2 Additional references
– ISO International Register of Coded Character Sets to be used with Escape Sequences.
– ISO/IEC 2022:1994, Information technology – Character code structure and extension techniques.
– ISO/IEC 2375:2003, Information technology – Procedure for registration of escape sequences and coded
character sets.
Rec. ITU-T X.690 (02/2021) 1
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– ISO 6093:1985, Information processing – Representation of numerical values in character strings for
information interchange.
– ISO/IEC 6429:1992, Information technology – Control functions for coded character sets.
– ISO/IEC 10646:2003, Information technology – Universal Multiple-Octet Coded Character Set (UCS).
3 Definitions
For the purposes of this Recommendation | International Standard, the definitions of Rec. ITU-T X.200 | ISO/IEC 7498-1 and
Rec. ITU-T X.680 | ISO/IEC 8824-1 and the following definitions apply.
3.1 canonical encoding: A complete encoding of an abstract value obtained by the application of encoding rules that
have no implementation-dependent options. Such rules result in the definition of a 1-1 mapping between unambiguous and
unique encodings and values in the abstract syntax.
3.2 constructed encoding: A data value encoding in which the contents octets are the complete encoding of one or
more data values.
3.3 contents octets: That part of a data value encoding which represents a particular value, to distinguish it from other
values of the same type.
3.4 data value: Information specified as the value of a type; the type and the value are defined using ASN.1.
3.5 dynamic conformance: A statement of the requirement for an implementation to adhere to the prescribed behaviour
in an instance of communication.
3.6 encoding (of a data value): The complete sequence of octets used to represent the data value.
3.7 end-of-contents octets: Part of a data value encoding, occurring at its end, which is used to determine the end of
the encoding.
NOTE – Not all encodings require end-of-contents octets.
3.8 identifier octets: Part of a data value encoding which is used to identify the type of the value.
NOTE – Some ITU-T Recommendations use the term "data element" for this sequence of octets, but the term is not used in this
Recommendation | International Standard, as other Recommendations | International Standards use it to mean "data value".
3.9 length octets: Part of a data value encoding following the identifier octets which is used to determine the end of the
encoding.
3.10 primitive encoding: A data value encoding in which the contents octets directly represent the value.
3.11 receiver: An implementation decoding the octets produced by a sender, in order to identify the data value which
was encoded.
3.12 sender: An implementation encoding a data value for transfer.
3.13 static conformance: A statement of the requirement for support by an implementation of a valid set of features
from among the defined features.
3.14 trailing 0 bit: A 0 in the last position of a bitstring value.
NOTE – The 0 in a bitstring value consisting of a single 0 bit is a trailing 0 bit. Its removal produces an empty bitstring.
4 Abbreviations
For the purposes of this Recommendation | International Standard, the following abbreviations apply:
ASN.1 Abstract Syntax Notation One
BER Basic Encoding Rules of ASN.1
CER Canonical Encoding Rules of ASN.1
DER Distinguished Encoding Rules of ASN.1
ULA Upper Layer Architecture
2 Rec. ITU-T X.690 (02/2021)
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UTF8 Universal Transformation Function 8-bit (see ISO/IEC 10646, Annex D)
5 Notation
This Recommendation | International Standard references the notation defined by Rec. ITU-T X.680 | ISO/IEC 8824-1.
6 Convention
6.1 This Recommendation | International Standard specifies the value of each octet in an encoding by use of the terms
"most significant bit" and "least significant bit".
NOTE – Lower layer specifications use the same notation to define the order of bit transmission on a serial line, or the assignment of
bits to parallel channels.
6.2 For the purposes of this Recommendation | International Standard only, the bits of an octet are numbered from 8 to
1, where bit 8 is the "most significant bit", and bit 1 is the "least significant bit".
6.3 For the purpose of this Recommendation | International Standard, two octet strings can be compared. One octet
string is equal to another if they are of the same length and are the same at each octet position. An octet string, S , is greater
than another, S , if and only if either:
a) S and S have identical octets in every position up to and including the final octet in S , but S is longer; or
1 2 2 1
b) S and S have different octets in one or more positions, and in the first such position, the octet in S is greater
1 2 1
n–1
than that in S , considering the octets as unsigned binary numbers whose bit n has weight 2 .
7 Conformance
7.1 Dynamic conformance is specified by clauses 8 to 12 inclusive.
7.2 Static conformance is specified by those standards which specify the application of one or more of these encoding
rules.
7.3 Alternative encodings are permitted by the basic encoding rules as a sender's option. Receivers who claim
conformance to the basic encoding rules shall support all alternatives.
NOTE – Examples of such alternative encodings appear in 8.1.3.2 b) and Table 3.
7.4 No alternative encodings are permitted by the Canonical Encoding Rules or Distinguished Encoding Rules.
8 Basic encoding rules
8.1 General rules for encoding
8.1.1 Structure of an encoding
8.1.1.1 The encoding of a data value shall consist of four components which shall appear in the following order:
a) identifier octets (see 8.1.2);
b) length octets (see 8.1.3);
c) contents octets (see 8.1.4);
d) end-of-contents octets (see 8.1.5).
8.1.1.2 The end-of-contents octets shall not be present unless the value of the length octets requires them to be present (see
8.1.3).
Rec. ITU-T X.690 (02/2021) 3
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8.1.1.3 Figure 1 illustrates the structure of an encoding (primitive or constructed). Figure 2 illustrates an alternative
constructed encoding.
Figure 1 – Structure of an encoding

Figure 2 – An alternative constructed encoding
8.1.1.4 Encodings specified in this Recommendation | International Standard are not affected by either the ASN.1 subtype
notation or the ASN.1 type extensibility notation.
NOTE – This means that all constraint notation is ignored when determining encodings, and all extensibility markers in CHOICE,
SEQUENCE and SET are ignored, with the extensions treated as if they were in the extension root of the type.
8.1.1.5 There are no encoding instructions (see Rec. ITU-T X.680 | ISO/IEC 8824-1, 3.8.27) defined for the encoding rules
specified in this Recommendation | International Standard.
8.1.2 Identifier octets
8.1.2.1 The identifier octets shall encode the ASN.1 tag (class and number) of the type of the data value.
8.1.2.2 For tags with a number ranging from zero to 30 (inclusive), the identifier octets shall comprise a single octet encoded
as follows:
a) bits 8 and 7 shall be encoded to represent the class of the tag as specified in Table 1;
b) bit 6 shall be a zero or a one according to the rules of 8.1.2.5;
c) bits 5 to 1 shall encode the number of the tag as a binary integer with bit 5 as the most significant bit.
Table 1 – Encoding of class of tag
Class Bit 8 Bit 7
Universal 0 0
Application 0 1
Context-specific 1 0
Private 1 1
4 Rec. ITU-T X.690 (02/2021)
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8.1.2.3 Figure 3 illustrates the form of an identifier octet for a type with a tag whose number is in the range zero
to 30 (inclusive).
Figure 3 – Identifier octet (low tag number)
8.1.2.4 For tags with a number greater than or equal to 31, the identifier shall comprise a leading octet followed by one or
more subsequent octets.
8.1.2.4.1 The leading octet shall be encoded as follows:
a) bits 8 and 7 shall be encoded to represent the class of the tag as listed in Table 1;
b) bit 6 shall be a zero or a one according to the rules of 8.1.2.5;
c) bits 5 to 1 shall be encoded as 11111 .
8.1.2.4.2 The subsequent octets shall encode the number of the tag as follows:
a) bit 8 of each octet shall be set to one unless it is the last octet of the identifier octets;
b) bits 7 to 1 of the first subsequent octet, followed by bits 7 to 1 of the second subsequent octet, followed in turn
by bits 7 to 1 of each further octet, up to and including the last subsequent octet in the identifier octets shall be
the encoding of an unsigned binary integer equal to the tag number, with bit 7 of the first subsequent octet as
the most significant bit;
c) bits 7 to 1 of the first subsequent octet shall not all be zero.
8.1.2.4.3 Figure 4 illustrates the form of the identifier octets for a type with a tag whose number is greater than 30.

Figure 4 – Identifier octets (high tag number)
8.1.2.5 Bit 6 shall be set to zero if the encoding is primitive, and shall be set to one if the encoding is constructed.
NOTE – Subsequent subclauses specify whether the encoding is primitive or constructed for each type.
8.1.2.6 Rec. ITU-T X.680 | ISO/IEC 8824-1 specifies that the tag of a type defined using the CHOICE keyword takes the
value of the tag of the type from which the chosen data value is taken.
8.1.2.7 Rec. ITU-T X.681 | ISO/IEC 8824-2, 14.2 and 14.4, specifies that the tag of a type defined using
"ObjectClassFieldType" is indeterminate if it is a type field, a variable-type value field, or a variable-type value set field. This
type is subsequently defined to be an ASN.1 type, and the complete encoding is then identical to that of a value of the assigned
type (including the identifier octets).
8.1.3 Length octets
8.1.3.1 Two forms of length octets are specified. These are:
a) the definite form (see 8.1.3.3); and
b) the indefinite form (see 8.1.3.6).
8.1.3.2 A sender shall:
Rec. ITU-T X.690 (02/2021) 5
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a) use the definite form (see 8.1.3.3) if the encoding is primitive;
b) use either the definite form (see 8.1.3.3) or the indefinite form (see 8.1.3.6), a sender's option, if the encoding
is constructed and all immediately available;
c) use the indefinite form (see 8.1.3.6) if the encoding is constructed and is not all immediately available.
8.1.3.3 For the definite form, the length octets shall consist of one or more octets, and shall represent the number of octets
in the contents octets using either the short form (see 8.1.3.4) or the long form (see 8.1.3.5) as a sender's option.
NOTE – The short form can only be used if the number of octets in the contents octets is less than or equal to 127.
8.1.3.4 In the short form, the length octets shall consist of a single octet in which bit 8 is zero and bits 7 to 1 encode the
number of octets in the contents octets (which may be zero), as an unsigned binary integer with bit 7 as the most significant
bit.
EXAMPLE
L = 38 can be encoded as 00100110
8.1.3.5 In the long form, the length octets shall consist of an initial octet and one or more subsequent octets. The initial
octet shall be encoded as follows:
a) bit 8 shall be one;
b) bits 7 to 1 shall encode the number of subsequent octets in the length octets, as an unsigned binary integer with
bit 7 as the most significant bit;
c) the value 11111111 shall not be used.
NOTE 1 – This restriction is introduced for possible future extension.
Bits 8 to 1 of the first subsequent octet, followed by bits 8 to 1 of the second subsequent octet, followed in turn by bits 8 to 1
of each further octet up to and including the last subsequent octet, shall be the encoding of an unsigned binary integer equal
to the number of octets in the contents octets, with bit 8 of the first subsequent octet as the most significant bit.
EXAMPLE
L = 201 can be encoded as:
NOTE 2 – In the long form, it is a sender's option whether to use more length octets than the minimum necessary.
8.1.3.6 For the indefinite form, the length octets indicate that the contents octets are terminated by end-of-contents octets
(see 8.1.5), and shall consist of a single octet.
8.1.3.6.1 The single octet shall have bit 8 set to one, and bits 7 to 1 set to zero.
8.1.3.6.2 If this form of length is used, then end-of-contents octets (see 8.1.5) shall be present in the encoding following the
contents octets.
8.1.4 Contents octets
The contents octets shall consist of zero, one or more octets, and shall encode the data value as specified in subsequent clauses.
NOTE – The contents octets depend on the type of the data value; subsequent clauses follow the same sequence as the definition of
types in ASN.1.
8.1.5 End-of-contents octets
The end-of-contents octets shall be present if the length is encoded as specified in 8.1.3.6, otherwise they shall not be present.
The end-of-contents octets shall consist of two zero octets.
NOTE – The end-of-contents octets can be considered as the encoding of a value whose tag is universal class, whose form is primitive,
whose number of the tag is zero, and whose contents are absent, thus:
End-of-contents Length Contents
00 00 Absent
16 16
6 Rec. ITU-T X.690 (02/2021)
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8.2 Encoding of a boolean value
8.2.1 The encoding of a boolean value shall be primitive. The contents octets shall consist of a single octet.
8.2.2 If the boolean value is:
FALSE
the octet shall be zero.
If the boolean value is
TRUE
the octet shall have any non-zero value, as a sender's option.
EXAMPLE
If of type BOOLEAN, the value TRUE can be encoded as:
Boolean Length Contents
01 01 FF
16 16 16
8.3 Encoding of an integer value
8.3.1 The encoding of an integer value shall be primitive. The contents octets shall consist of one or more octets.
8.3.2 If the contents octets of an integer value encoding consist of more than one octet, then the bits of the first octet and
bit 8 of the second octet:
a) shall not all be ones; and
b) shall not all be zero.
NOTE – These rules ensure that an integer value is always encoded in the smallest possible number of octets.
8.3.3 The contents octets shall be a two's complement binary number equal to the integer value, and consisting of bits 8
to 1 of the first octet, followed by bits 8 to 1 of the second octet, followed by bits 8 to 1 of each octet in turn up to and including
the last octet of the contents octets.
NOTE – The value of a two's complement binary number is derived by numbering the bits in the contents octets, starting with bit 1 of
N
the last octet as bit zero and ending the numbering with bit 8 of the first octet. Each bit is assigned a numerical value of 2 , where N is
its position in the above numbering sequence. The value of the two's complement binary number is obtained by summing the numerical
values assigned to each bit for those bits which are set to one, excluding bit 8 of the first octet, and then reducing this value by the
numerical value assigned to bit 8 of the first octet if that bit is set to one.
8.4 Encoding of an enumerated value
The encoding of an enumerated value shall be that of the integer value with which it is associated.
NOTE – It is primitive.
8.5 Encoding of a real value
8.5.1 The encoding of a real value shall be primitive.
8.5.2 If the real value is the value plus zero, there shall be no contents octets in the encoding.
8.5.3 If the real value is the value minus zero, then it shall be encoded as specified in 8.5.9.
8.5.4 For a non-zero real value, if the base of the abstract value is 10, then the base of the encoded value shall be 10, and
if the base of the abstract value is 2 the base of the encoded value shall be 2, 8 or 16 as a sender's option.
8.5.5 If the real value is non-zero, then the base used for the encoding shall be B' as specified in 8.5.4. If B' is 2, 8 or 16,
a binary encoding, specified in 8.5.7, shall be used. If B' is 10, a character encoding, specified in 8.5.8, shall be used.
8.5.6 Bit 8 of the first contents octet shall be set as follows:
a) if bit 8 = 1, then the binary encoding specified in 8.5.7 applies;
Rec. ITU-T X.690 (02/2021) 7
© ISO/IEC 2021 – All rights reserved

b) if bit 8 = 0 and bit 7 = 0, then the decimal encoding specified in 8.5.8 applies;
c) if bit 8 = 0 and bit 7 = 1, then either a "SpecialRealValue" (see Rec. ITU-T X.680 | ISO/IEC 8824-1) or the
value minus zero is encoded as specified in 8.5.9.
8.5.7 When binary encoding is used (bit 8 = 1), then if the mantissa M is non-zero, it shall be represented by a sign S, a
positive integer value N and a binary scaling factor F, such that:
F
M = S  N  2
0  F < 4
S = +1 or –1
NOTE – The binary scaling factor F is required under certain circumstances in order to align the implied point of the mantissa to the
position required by the encoding rules of this subclause. This alignment cannot always be achieved by modification of the exponent
E. If the base B' used for encoding is 8 or 16, the implied point can only be moved in steps of 3 or 4 bits, respectively, by changing the
component E. Therefore, values of the binary scaling factor F other than zero may be required in order to move the implied point to the
required position.
8.5.7.1 Bit 7 of the first contents octets shall be 1 if S is –1 and 0 otherwise.
8.5.7.2 Bits 6 to 5 of the first contents octets shall encode the value of the base B' as follows:
Bits 6 to 5 Base
00 base 2
01 base 8
10 base 16
11 Reserved for further editions of this Recommendation | International Standard.
8.5.7.3 Bits 4 to 3 of the first contents octet shall encode the value of the binary scaling factor F as an unsigned binary
integer.
8.5.7.4 Bits 2 to 1 of the first contents octet shall encode the format of the exponent as follows:
a) if bits 2 to 1 are 00, then the second contents octet encodes the value of the exponent as a two's complement
binary number;
b) if bits 2 to 1 are 01, then the second and third contents octets encode the value of the exponent as a two's
complement binary number;
c) if bits 2 to 1 are 10, then the second, third and fourth contents octets encode the value of the exponent as a
two's complement binary number;
d) if bits 2 to 1 are 11, then the second contents octet encodes the number of octets, X say, (as an unsigned binary
th
number) used to encode the value of the exponent, and the third up to the (X plus 3) (inclusive) contents
octets encode the value of the exponent as a two's complement binary number; the value of X shall be at least
one; the first nine bits of the transmitted exponent shall not be all zeros or all ones.
8.5.7.5 The remaining contents octets encode the value of the integer N (see 8.5.7) as an unsigned binary number.
NOTE 1 – For non-canonical BER there is no requirement for floating point normalization of the mantissa. This allows an implementer
to transmit octets containing the mantissa without performing shift functions on the mantissa in memory. In the Canonical Encoding
Rules and the Distinguished Encoding Rules normalization is specified and the mantissa (unless it is 0) needs to be repeatedly shifted
until the least significant bit is a 1.
NOTE 2 – This representation of real numbers is very different from the formats normally used in floating point hardware, but has been
designed to be easily converted to and from such formats (see Annex C).
8.5.8 When decimal encoding is used (bits 8 to 7 = 00), all the contents octets following the first contents octet form a
field, as the term is used in ISO 6093, of a length chosen by the sender, and encoded according to ISO 6093. The choice of
ISO 6093 number representation is specified by bits 6 to 1 of the first contents octet as follows:
Bits 6 to 1 Number representation
00 0001 ISO 6093 NR1 form
00 0010 ISO 6093 NR2 form
00 0011 ISO 6093 NR3 form
The remaining values of bits 6 to 1 are reserved for further editions of this Recommendation | International Standard.
8 Rec. ITU-T X.690 (02/2021)
© ISO/IEC 2021 – All rights reserved

There shall be no use of scaling factors specified in accompanying documentation (see ISO 6093).
NOTE 1 – The recommendations in ISO 6093 concerning the use of at least one digit to the left of the decimal mark are also
recommended in this Recommendation | International Standard, but are not mandatory.
NOTE 2 – Use of the normalized form (see ISO 6093) is a sender's option, and has no significance.
8.5.9 When "SpecialRealValues" or minus zero are to be encoded (bits 8 to 7 = 01), there shall be only one contents octet,
with values as follows:
01000000 Value is PLUS-INFINITY
01000001 Value is MINUS-INFINITY
01000010 Value is NOT-A-NUMBER
01000011 Value is minus zero
All other values having bits 8 and 7 equal to 0 and 1 respectively are reserved for addenda to this Recommendation |
International Standard.
8.6 Encoding of a bitstring value
8.6.1 The encoding of a bitstring value shall be either primitive or constructed at the option of the sender.
NOTE – Where it is necessary to transfer part of a bit string before the entire bitstring is available, the constructed encoding is used.
8.6.2 The contents octets for the primitive encoding shall contain an initial octet followed by zero, one or more subsequent
octets.
8.6.2.1 The bits in the bitstring value, commencing with the leading bit and proceeding to the trailing bit, shall be placed in
bits 8 to 1 of the first subsequent octet, followed by bits 8 to 1 of the second subsequent octet, followed by bits 8 to 1 of each
octet in turn, followed by as many bits as are needed of the final subsequent octet, commencing with bit 8.
NOTE – The terms "leading bit" and "trailing bit" are defined in Rec. ITU-T X.680 | ISO/IEC 8824-1, 22.2.
8.6.2.2 The initial octet shall encode, as an unsigned binary integer with bit 1 as the least significant bit, the number of
unused bits in the final subsequent octet. The number shall be in the range zero to seven.
8.6.2.3 If the bitstring is empty, there shall be no subsequent octets, and the initial octet shall be zero.
8.6.2.4 Where Rec. ITU-T X.680 | ISO/IEC 8824-1, 22.7, applies a BER encoder/decoder can add or remove trailing 0 bits
from the value.
NOTE – If a bitstring value has no 1 bits, then an encoder (as a sender's option) may encode the value with a length of 1 and with an
initial octet set to 0 or may encode it as a bit string with one or more 0 bits following the initial octet.
8.6.3 The contents octets for the constructed encoding shall consist of zero, one, or more nested encodings.
NOTE – Each such encoding includes identifier, length, and contents octets, and may include end-of-contents octets if it is constructed.
8.6.4 To encode a bitstring value in this way, it is segmented. Each segment shall consist of a series of con
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