Chen—Ho encoding is a memory-efficient alternate system of binary encoding for decimal digits. The traditional system of binary encoding for decimal digits, known as binary-coded decimal BCDuses four bits to encode each digit, resulting in significant wastage of binary data bandwidth since four bits can store 16 states and are being used to store only The encoding reduces the storage requirements of two decimal digits states from 8 to 7 bits, and those of three decimal digits states from 12 to 10 bits using only simple Boolean transformations avoiding any complex arithmetic operations like a base conversion.

In what appears to have been a multiple discoverysome of the concepts behind what later became known as Chen—Ho encoding were independently developed by Theodore M. Hertz in [2] and by Tien Chi Chen in Hertz of Rockwell filed a patent for his encoding inwhich was granted in Chen first discussed his ideas with Irving Tze Ho [4] in Chen and Ho were both working for IBM at the time, although in different locations.

Tung [7] to verify the results of his theories independently. It constitutes a Huffman -like prefix code. The encoding became known as Chen—Ho encoding or Chen—Ho algorithm only since Chen noted that the digits zero through seven were simply encoded using three binary digits of the corresponding octal group.

**Binary Numbers and Base Systems as Fast as Possible**

He also postulated that one could use a flag to identify a different encoding for the digits eight and nine, which would be encoded using a single bit. In practice, a series of Boolean transformations are applied to the stream of input bits, compressing BCD encoded digits from 12 bits per three digits to 10 bits per three digits.

Reversed transformations are used to decode the resulting coded stream to BCD. Equivalent results can also be achieved by the use of a look-up table. Chen—Ho encoding is limited to encoding sets of three decimal digits into groups of 10 bits so called declets. With only 0. Both Hertz and Chen also proposed similar, but less efficient, encoding schemes to compress sets of two decimal digits requiring 8 bits in BCD into groups of 7 bits.

Larger sets of decimal digits could by divided into three- and two-digit groups. The patents also discuss the possibility to adapt the scheme to digits encoded in any other decimal codes than BCD, like f. One prominent application uses a bit register to store 33 decimal digits with a three digit exponent, effectively not less than what could be achieved using binary encoding whereas BCD encoding would need bits to store the same number of digits.

From Wikipedia, the free encyclopedia. Handbook of Floating-Point Arithmetic 1 ed. Retrieved A coding system very similar to Chen-Ho, also cited as prior art in the Chen—Ho patent.

Archived from the original on Taiwan Info. Decimal-binary integer conversion scheme Internal memo to Irving Tze Ho. Archived PDF from the original on This patent is about the Chen—Ho algorithm. Research Report RJ Technical report. Communications of the ACM. June []. GA File No. Categories : Binary arithmetic. Hidden categories: Articles with short description Use dmy dates from May Binary data is a sequence of 8 bit bytes, where each byte can have a value between 0x00 and 0xFF.

ASCII data represents text as a sequence of bytes. Since ASCII data is not expected to contain byte values of 0x80 or greater ie with the most significant bit setit is often called 7 bit data. If a system is designed to handle text data, it might make certain assumptions about that data. This can easily cause the system to fail if binary data is passed through it.

Here are some of the most common problems:. Line endings - different computer operating systems have different conventions for representing line endings. Some systems try to be helpful by automatically substituting these characters.

This is great for genuine text data, but absolutely disastrous for binary data. Tab substitution - in a similar way, some systems automatically substitute tab characters for multiple spaces, or vice versa. Special characters - some systems assign special meanings to particular non-printable characters. Some systems even emit a beep when they encounter the BEL character 0x07!

Line length - some systems process text on a line by line basis, and they often make assumptions about how long text lines will be eg 80 characters maximum. If a file is encountered where the lines are too long, it might lead to data loss, program errors, or even a crash. But in a binary file, there is no reason to suppose that these characters will appear regularly, if at all.

Rejection - some systems scan the data for non-text characters, and simply refuse to process binary data. We have listed some of the possible problems with processing binary data in a text based system.

Of course some systems are more robust than others, but you are likely to encounter one or more of these types of problems in many cases. A solution to this problem is to use binary encoding. Before passing our binary data through a text based system, we encode as a longer sequence of text characters. When we get the data back out of the system, we must decode it to obtain our original data.

We obviously need to be careful about whitespace characters, because they might not be transferred reliably. On the other hand they are clearly necessary CR or LF are needed to split the data into manageable line lengths. Most encoding schemes use only printable characters for encoding but allow line breaks to be present but ignore them when decoding. Home Graphics Computer music Legacy articles. What is binary encoding, and why is it useful?

All is explained here. Problems with Binary Data If a system is designed to handle text data, it might make certain assumptions about that data.

Here are some of the most common problems: Line endings - different computer operating systems have different conventions for representing line endings. A Solution — Binary Encoding We have listed some of the possible problems with processing binary data in a text based system.Package binary implements simple translation between numbers and byte sequences and encoding and decoding of varints.

Numbers are translated by reading and writing fixed-size values. A fixed-size value is either a fixed-size arithmetic type bool, int8, uint8, int16, float32, complex64, The varint functions encode and decode single integer values using a variable-length encoding; smaller values require fewer bytes.

This package favors simplicity over efficiency. PutUvarint encodes a uint64 into buf and returns the number of bytes written. If the buffer is too small, PutUvarint will panic. PutVarint encodes an int64 into buf and returns the number of bytes written. If the buffer is too small, PutVarint will panic. Read reads structured binary data from r into data.

Data must be a pointer to a fixed-size value or a slice of fixed-size values. Bytes read from r are decoded using the specified byte order and written to successive fields of the data. When decoding boolean values, a zero byte is decoded as false, and any other non-zero byte is decoded as true. When reading into a struct, all non-blank fields must be exported or Read may panic.

The error is EOF only if no bytes were read. Size returns how many bytes Write would generate to encode the value v, which must be a fixed-size value or a slice of fixed-size values, or a pointer to such data.

If v is neither of these, Size returns Write writes the binary representation of data into w. Data must be a fixed-size value or a slice of fixed-size values, or a pointer to such data. Boolean values encode as one byte: 1 for true, and 0 for false. Bytes written to w are encoded using the specified byte order and read from successive fields of the data. Package binary.

### binary encoding

ByteReader uint64, error func ReadVarint r io. Examples Expand All. PutUvarint buf, x fmt.This article addresses the encoding of, and the data types used, for the state register. The encoding of the states of an FSM affects its performance in terms of speed, resource usage registers, logic and potentially power consumption.

As we will see, enumerated datatypes are preferred for clarity and easy of maintenance. The preferred encoding depends on the nature of the design.

### Binary Encoding

Binary encoding minimizes the length of the state vector, which is good for CPLD designs. One-hot encoding is usually faster and uses more registers and less logic. That makes one-hot encoding more suitable for FPGA designs where registers are usually abundant. Gray encoding will reduce glitches in an FSM with limited or no branches. Generally speaking, a state register can be implemented in two different ways: either as a vector type or as an enumeration type.

With a vector typethe designer has perfect control over the encoding of the state vector. However, it is hard to know what each state means and changes are cumbersome. If a state needs to be inserted, the encoding of all further states need to be updated wherever used. With an enumeration typethe design becomes much easier to understand and maintain :. States can be added or modified easily, and other states are not affected when one state is added or modified.

The encoding of the states however is magically implemented by the RTL synthesis tool. Fortunately, most RTL synthesis tools have ways for the designer to control the state encoding of enumerated state types. In many cases, one would like to define the state encoding style. The example below shows how that can be achieved at the type level :.

Support of enumeration encoding styles differs between RTL synthesis toolsso have a look at the manual of yours for supported styles. Also, some RTL synthesis tools e. Alternatively, the state encoding style can be defined at the signal level rather than at the type level. This way, multiple FSMs with the same set of states can each have a different state encoding. In the above examples, only the encoding style of the state vector is defined.

If a state is added, its encoding needs to be added in the attribute. The example below shows how that can be achieved. In conclusion, enumerated types are preferred for FSM state vectors. Well chosen enumeration literals make the FSM more easy to read, understand and maintain.

With an enumerated type, states can be added to or removed from the FSM without affecting the other states. The size of the state vector will be adjusted during RTL synthesis. Still, the designer retains as much control of the state encoding as they desire. Support Jobs News Contact. Sigasi Studio 4. Sigasi Studio Preview 4. Use a Word macro to Scale Diagrams in html documentation.A binary code represents textcomputer processor instructionsor any other data using a two-symbol system.

The two-symbol system used is often "0" and "1" from the binary number system. The binary code assigns a pattern of binary digits, also known as bitsto each character, instruction, etc. For example, a binary string of eight bits can represent any of possible values and can, therefore, represent a wide variety of different items.

In computing and telecommunications, binary codes are used for various methods of encoding data, such as character stringsinto bit strings. Those methods may use fixed-width or variable-width strings.

In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a binary numberis usually displayed in code tables in octaldecimal or hexadecimal notation. There are many character sets and many character encodings for them. A bit stringinterpreted as a binary number, can be translated into a decimal number. For example, the lower case aif represented by the bit string as it is in the standard ASCII codecan also be represented as the decimal number "97".

The full title is translated into English as the "Explanation of the binary arithmetic", which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi. Leibniz's system uses 0 and 1, like the modern binary numeral system. Leibniz encountered the I Ching through French Jesuit Joachim Bouvet and noted with fascination how its hexagrams correspond to the binary numbers from 0 toand concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical visual binary mathematics he admired.

Binary numerals were central to Leibniz's theology. He believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. The book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system.

Binary systems predating Leibniz also existed in the ancient world. The residents of the island of Mangareva in French Polynesia were using a hybrid binary- decimal system before The ordering is also the lexicographical order on sextuples of elements chosen from a two-element set. In Francis Bacon discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.

George Boole published a paper in called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as Boolean algebra. Shannon wrote his thesis inwhich implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more.

The bit string is not the only type of binary code: in fact, a binary system in general, is any system that allows only two choices such as a switch in an electronic system or a simple true or false test.

Braille is a type of binary code that is widely used by the blind to read and write by touch, named for its creator, Louis Braille.This document describes the portable binary encoding of the WebAssembly modules.

The binary encoding is a dense representation of module information that enables small files, fast decoding, and reduced memory usage. See the rationale document for more detail. Most importantly, the layering approach allows development and standardization to occur incrementally.

For example, Layer 1 and Layer 2 encoding techniques can be experimented with by application-level decompressing to the layer below. As compression techniques stabilize, they can be standardized and moved into native implementations. See proposed layer 1 compression for a proposal for layer 1 structural compression. N is either 8, 16, or A LEB variable-length integer, limited to N bits i. Note: Currently, the only sizes used are varuint1varuint7and varuint32where the former two are used for compatibility with potential future extensions.

Note: Currently, the only sizes used are varint7varint32 and varint In the MVP, the opcodes of instructions are all encoded in a single byte since there are fewer than opcodes. Future features like SIMD and atomics will bring the total count above and so an extension scheme will be necessary, designating one or more single-byte values as prefixes for multi-byte opcodes. All types are distinguished by a negative varint7 values that is the first byte of their encoding representing a type constructor :.

Note: Gaps are reserved for future extensions. The use of a signed scheme is so that types can coexist in a single space with positive indices into the type section, which may be relevant for future extensions of the type system.

## Chen–Ho encoding

A varint7 indicating a value type. One of:. A varint7 indicating a block signature. These types are encoded as:. A varint7 indicating the types of elements in a table. In the MVP, only one type is available:. Note: In the futureother element types may be allowed. The description of a function signature. Its type constructor is followed by an additional description:. A packed tuple that describes the limits of a table or memory :.

The encoding of an initializer expression is the normal encoding of the expression followed by the end opcode as a delimiter. The following documents the current prototype format.

This format is based on and supersedes the v8-native prototype format, originally in a public design doc. The module preamble is followed by a sequence of sections. Each section is identified by a 1-byte section code that encodes either a known section or a custom section. The section length and payload data then follow. Known sections have non-zero ids, while custom sections have a 0 id followed by an identifying string as part of the payload.

Each known section is optional and may appear at most once.This document describes the binary wire format for protocol buffer messages. You don't need to understand this to use protocol buffers in your applications, but it can be very useful to know how different protocol buffer formats affect the size of your encoded messages. You then serialize the message to an output stream.

If you were able to examine the encoded message, you'd see three bytes: 08 96 01 So far, so small and numeric — but what does it mean? Read on Base Varints To understand your simple protocol buffer encoding, you first need to understand varints. Varints are a method of serializing integers using one or more bytes. Smaller numbers take a smaller number of bytes. Each byte in a varint, except the last byte, has the most significant bit msb set — this indicates that there are further bytes to come.

The lower 7 bits of each byte are used to store the two's complement representation of the number in groups of 7 bits, least significant group first. So, for example, here is the number 1 — it's a single byte, so the msb is not set: And here is — this is a bit more complicated: How do you figure out that this is ?

The binary version of a message just uses the field's number as the key — the name and declared type for each field can only be determined on the decoding end by referencing the message type's definition i.

When a message is encoded, the keys and values are concatenated into a byte stream. When the message is being decoded, the parser needs to be able to skip fields that it doesn't recognize. This way, new fields can be added to a message without breaking old programs that do not know about them. To this end, the "key" for each pair in a wire-format message is actually two values — the field number from your.

## Text.FromBinary

In most language implementations this key is referred to as a tag. Now let's look at our simple example again. You now know that the first number in the stream is always a varint key, and here it's 08, or dropping the msb : You take the last three bits to get the wire type 0 and then right-shift by three to get the field number 1. So you now know that the field number is 1 and the following value is a varint. Using your varint-decoding knowledge from the previous section, you can see that the next two bytes store the value However, there is an important difference between the signed int types sint32 and sint64 and the "standard" int types int32 and int64 when it comes to encoding negative numbers.

If you use int32 or int64 as the type for a negative number, the resulting varint is always ten bytes long — it is, effectively, treated like a very large unsigned integer. If you use one of the signed types, the resulting varint uses ZigZag encoding, which is much more efficient.

ZigZag encoding maps signed integers to unsigned integers so that numbers with a small absolute value for instance, -1 have a small varint encoded value too. So, in other words, the result of the shift is either a number that is all zero bits if n is positive or all one bits if n is negative.

## thoughts on “Binary encoding”