Nibble

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An octet code page 866 font table ordered by nibbles. Octets in CP866 ordered by nibbles.png
An octet code page 866 font table ordered by nibbles.

In computing, a nibble [1] (occasionally nybble or nyble to match the spelling of byte) is a four-bit aggregation, [1] [2] [3] or half an octet. It is also known as half-byte [4] or tetrade. [5] [6] In a networking or telecommunication context, the nibble is often called a semi-octet, [7] quadbit, [8] or quartet. [9] [10] A nibble has sixteen (24) possible values. A nibble can be represented by a single hexadecimal digit and called a hex digit. [11]

Contents

A full byte (octet) is represented by two hexadecimal digits; therefore, it is common to display a byte of information as two nibbles. Sometimes the set of all 256 byte values is represented as a 16×16 table, which gives easily readable hexadecimal codes for each value.

Four-bit computer architectures use groups of four bits as their fundamental unit. Such architectures were used in early microprocessors, pocket calculators and pocket computers. They continue to be used in some microcontrollers. In this context, 4-bit groups were sometimes also called characters [12] rather than nibbles. [1]

History

The term 'nibble' originates from its representing 'half a byte', with 'byte' a homophone of the English word 'bite'. [4] In 2014, David B. Benson, a professor emeritus at Washington State University, remembered that he playfully used (and may have possibly coined) the term nibble as "half a byte" and unit of storage required to hold a binary-coded decimal (BCD) decimal digit around 1958, when talking to a programmer of Los Alamos Scientific Laboratory. The alternative spelling 'nybble' reflects the spelling of 'byte', as noted in editorials of Kilobaud and Byte in the early 1980s. Another early recorded use of the term 'nybble' was in 1977 within the consumer-banking technology group at Citibank. It created a pre-ISO 8583 standard for transactional messages between cash machines and Citibank's data centers that used the basic informational unit 'NABBLE'.

The nibble is used to describe the amount of memory used to store a digit of a number stored in packed decimal format (BCD) within an IBM mainframe. This technique is used to make computations faster and debugging easier. An 8-bit byte is split in half and each nibble is used to store one decimal digit. The last (rightmost) nibble of the variable is reserved for the sign. Thus a variable which can store up to nine digits would be "packed" into 5 bytes. Ease of debugging resulted from the numbers being readable in a hex dump where two hex numbers are used to represent the value of a byte, as 16×16 = 28. For example, a five-byte BCD value of 31 41 59 26 5C represents a decimal value of +314159265.

Historically, there are cases where nybble was used for a group of bits greater than 4. In the Apple II microcomputer line, much of the disk drive control and group-coded recording was implemented in software. Writing data to a disk was done by converting 256-byte pages into sets of 5-bit (later, 6-bit) nibbles and loading disk data required the reverse. [13] [14] [15] Moreover, 1982 documentation for the Integrated Woz Machine refers consistently to an "8 bit nibble". [16] The term byte once had the same ambiguity and meant a set of bits but not necessarily 8, hence the distinction of bytes and octets or of nibbles and quartets (or quadbits). Today, the terms 'byte' and 'nibble' almost always refer to 8-bit and 4-bit collections respectively and are very rarely used to express any other sizes.

Table of nibbles

The sixteen nibbles and their equivalents in other numeral systems:

Examples
BinaryHexadecimal
0000 0100 00100 4 2
0010 1010 10012 A 9
0010 0000 10012 0 9
1110 0100 1001E 4 9
0011 1001 01103 9 6
0001 0000 00011 0 1
0011 0101 01003 5 4
0001 0110 01001 6 4
0hex= 0dec =0oct0000
1hex= 1dec =1oct0001
2hex= 2dec =2oct0010
3hex= 3dec =3oct0011
4hex= 4dec =4oct0100
5hex= 5dec =5oct0101
6hex= 6dec =6oct0110
7hex= 7dec =7oct0111
8hex= 8dec =10oct1000
9hex= 9dec =11oct1001
Ahex= 10dec =12oct1010
Bhex= 11dec =13oct1011
Chex= 12dec =14oct1100
Dhex= 13dec =15oct1101
Ehex= 14dec =16oct1110
Fhex= 15dec =17oct1111

Low and high nibbles

The terms "low nibble" and "high nibble" are used to denote the nibbles containing, respectively, the less significant bits and the more significant bits within a byte. In graphical representations of bits within a byte, the leftmost bit could represent the most significant bit (MSB), corresponding to ordinary decimal notation in which the digit at the left of a number is the most significant. In such illustrations the four bits on the left end of the byte form the high nibble, and the remaining four bits form the low nibble. [17] For example,

ninety-seven = 9710 = (0110 0001)2 = 61hex

the high nibble is 01102 (6hex), and the low nibble is 00012 (1hex). The total value is high-nibble × 1610 + low-nibble (6×16+1=9710).

Extracting a nibble from a byte

A nibble can be extracted from a byte by doing a bitwise logical AND operation and optionally a bit shift depending on if the high or low nibble is to be extracted.

In C:

#define HI_NIBBLE(b) (((b) >> 4) & 0x0F)#define LO_NIBBLE(b) ((b) & 0x0F)

where b must be a variable or constant of an integral data type, and only the least-significant byte of b is used.

For example, HI_NIBBLE(0xAB)==0xA and LO_NIBBLE(0xAB)==0xB.

In Common Lisp:

(defunhi-nibble(b)(ldb(byte44)b))(defunlo-nibble(b)(ldb(byte40)b))

See also

Related Research Articles

The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness. The first bit is number 0, making the eighth bit number 7.

Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications.

In mathematics and computing, the hexadecimal numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the common way of representing numbers using 10 symbols, hexadecimal uses 16 distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" to represent values 10 to 15.

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provide a way to represent a processor register or memory address as an integer.

A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.

In computer architecture, 4-bit integers, or other data units are those that are 4 bits wide. Also, 4-bit CPU and ALU architectures are those that are based on registers, or data buses of that size. Memory addresses (and thus address buses) for 4-bit CPUs are generally much larger than 4-bit (since only 16 memory locations would be very restrictive), such as 12-bit or more, while they could in theory be 8-bit. A group of four bits is also called a nibble and has 24 = 16 possible values.

An organizationally unique identifier (OUI) is a 24-bit number that uniquely identifies a vendor, manufacturer, or other organization.

A hex editor is a computer program that allows for manipulation of the fundamental binary data that constitutes a computer file. The name 'hex' comes from 'hexadecimal': a standard numerical format for representing binary data. A typical computer file occupies multiple areas on the storage medium, whose contents are combined to form the file. Hex editors that are designed to parse and edit sector data from the physical segments of floppy or hard disks are sometimes called sector editors or disk editors.

The Intel BCD opcodes are a set of six x86 instructions that operate with binary-coded decimal numbers. The radix used for the representation of numbers in the x86 processors is 2. This is called a binary numeral system. However, the x86 processors do have limited support for the decimal numeral system.

Intel hexadecimal object file format, Intel hex format or Intellec Hex is a file format that conveys binary information in ASCII text form. It is commonly used for programming microcontrollers, EPROMs, and other types of programmable logic devices. In a typical application, a compiler or assembler converts a program's source code to machine code and outputs it into a HEX file. Common file extensions used for the resulting files are .HEX or .H86. The HEX file is then read by a programmer to write the machine code into a PROM or is transferred to the target system for loading and execution.

The octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes.

HP Saturn Family of 4-bit datapath microprocessors

The Saturn family of 4-bit microprocessors was developed by Hewlett-Packard in the 1980s first for the HP-71B handheld computer and then later for various HP calculators. It succeeded the Nut family of processors used in earlier calculators. The original Saturn chip was first used in the HP-71B hand-held BASIC-programmable computer, introduced in 1984. Later models of the family powered the popular HP 48 series of calculators. The HP48SX and HP48S were the last models to use genuine Saturn processors manufactured by HP. Later calculator models used Saturn processors manufactured by NEC. The HP 49 series initially used the Saturn CPU as well, until the NEC fab could no longer manufacture the processor for technical reasons in 2003. Therefore, starting with the HP 49g+ model in 2003, the calculators switched to a Samsung S3C2410 processor with an ARM920T core which ran an emulator of the Saturn hardware in software. In 2000, the HP 39G and HP 40G were the last calculators introduced based on the actual NEC fabricated Saturn hardware. The last calculators based on the Saturn emulator were the HP 39gs, HP 40gs and HP 50g in 2006, as well as the 2007 revision of the hp 48gII. The HP 50g, the last calculator utilizing this emulator, was discontinued in 2015 when Samsung stopped producing the ARM processor on which it was based.

SREC (file format)

Motorola S-record is a file format, created by Motorola, that conveys binary information as hex values in ASCII text form. This file format may also be known as SRECORD, SREC, S19, S28, S37. It is commonly used for programming flash memory in microcontrollers, EPROMs, EEPROMs, and other types of programmable logic devices. In a typical application, a compiler or assembler converts a program's source code to machine code and outputs it into a HEX file. The HEX file is then imported by a programmer to "burn" the machine code into non-volatile memory, or is transferred to the target system for loading and execution.

In computing, bit numbering is the convention used to identify the bit positions in a binary number or a container of such a value. The bit number starts with zero and is incremented by one for each subsequent bit position.

Decimal computer

Decimal computers are computers which can represent numbers and addresses in decimal as well as providing instructions to operate on those numbers and addresses directly in decimal, without conversion to a pure binary representation. Some also had a variable wordlength, which enabled operations on numbers with a large number of digits.

In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure the entropy of random variables and information contained in messages.

Tektronix hex format and Extended Tektronix hex format / Extended Tektronix Object Format are ASCII-based hexadecimal file formats, created by Tektronix, for conveying binary information for applications like programming microcontrollers, EPROMs, and other kinds of chips.

BCD, also called alphanumeric BCD, alphameric BCD, BCD Interchange Code, or BCDIC, is a family of representations of numerals, uppercase Latin letters, and some special and control characters as six-bit character codes.

A half-carry flag is a condition flag bit in the status register of many CPU families, such as the Intel 8080, Zilog Z80, the x86, and the Atmel AVR series, among others. It indicates when a carry or borrow has been generated out of the least significant four bits of the accumulator register following the execution of an arithmetic instruction. It is primarily used in decimal (BCD) arithmetic instructions.

In computing, a hextet is a sixteen-bit aggregation, or four nibbles. As a nibble typically is notated in hexadecimal format, a hextet consists of 4 hexadecimal digits. A hextet is the unofficial name for each of the 8 blocks in an IPv6 address.

References

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