Q: How many binary digits does a single hexadecimal digit represent?

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You could first convert it to binary, and then to hexadecimal. Because octal and hexadecimal bases are both powers of two, the conversion between those bases and binary is quite easy. To go from octal to binary, take each digit in the number, and convert it to three binary digits: 5 -> 101 3 -> 011 2 -> 010 4 -> 100 So the binary version of the number is: 101 011 011 010 100 In order to convert to hexadecimal, your number of digits needs to be divisible by four (as 24 = 16). To get that, we need to add a digit, which will be a zero as our leftmost digit: 0101 0110 1101 0100 Now we can convert each of those sets of four binary digits into single hexadecimal digits, giving us our final answer: 9AD8

A "hextet" in IPv6 consists of 2 bytes, or 4 hexadecimal digits (as in the example in the question), or 16 bits.

Two. 0 and 1. Any system uses as many single digits as the nominal base. Base 10 uses 10: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Base 16 (hexadecimal) uses 16: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e and f. etc.

It was invented just like any other base system that uses place value columns: Each place value column is eight times bigger than the place value column to its right. There is no reason to use the base 10 system other than we normally have 2 thumbs and 8 fingers giving 10 digits on our hands. In fact the Babylonians used sexagesimal (base 60) numbers; their legacy can be seen in the degrees in a circle and in our measurement of time: the colon used to separate the digits of a 24 hour time in the format "hh:mm:ss" are separators of sexagesimal digits that are represented by the base 10 numbers 0-59 - times are just the number of seconds since midnight expressed as a sexagesimal number. Some cultures have used a base 20 number system. When it comes to digital computers, they tend to use binary numbers as each location of memory can store one of two states: 0 or 1; these are binary-digits or bits (for short). The bits are then grouped together: 4 bits make 1 nybble 2 nybbles = 8 bits = 1 byte. We're used to decimal numbers so 1 byte can store the binary numbers 0 - 1111 1111 = 0-255 (in decimal). Two bytes allow storage of 0 - 1111 1111 1111 1111 = 0-65535 (in decimal). This conversion from binary to decimal is not very easy; to overcome this Binary Coded Decimal (BCD) can be used. BCD only uses the binary patterns of decimal numbers, ie 0-9 = 0000-1001, thus a byte can now store two decimal digits 0-99 (but this is very wasteful). A much more useful representation of numbers in a digital computer is to use numbers with a base that is a power of 2 - that way every binary pattern is used. One such system is hexadecimal or base 16. In this case each digit of a number is a number in the range 0-15 in decimal; to make each digit occupy a single character, the letters a-f (in either lower case or upper case a A-F) are used for 10-15, so that each hexadecimal digit is 0-f. 15 (0xf) is represented in binary as 1111 - 4 bits or 1 nybble. This means that each hexadecimal digit is exactly half a byte, and so two hexadecimal digits represent a byte exactly; this makes writing numbers extremely efficient and easy to convert to binary. This ability to easily convert hexadecimal numbers to binary is useful for computer programmers as they will often use blocks of bits as flags. For example file permissions under *nix are a grouping of 3 bits: Read/Write/eXecute for different users. These permissions can be written easily into hexadecimal (for example 0x1ed) but it is not very obvious what the permissions are; however as there are three in each group it is better to use base 2³ = 8 numbers, or octal numbers. In octal each digit can contain the digits 0-7 (which avoids the need to create symbols for digits after the decimal digit 9). In the previous example of permissions 0x1ed (hexadecimal) = 0755 (octal) which is easily converted into the permissions rwxr-xr-x and the user know instantly what it means. Octal was not invented specifically as a number system; it just exists as one as a consequence of the invention of the place value system. However, the grouping of bits in digital computers makes it useful for some applications there.

1 is a single digit, 0 is the absence of a digit.

Related questions

Each 4-digit string of binary digits is equivalent to 1 single hexadecimal digit.

Hexadecimal number system is a number sytem with a Base of 16. The 'regular' system which we use every day is base-ten (decimal), with the digits 0-9.Having a base 16 system makes it easier to represent values of computer memory, as computers deal in binary (base 2), where every value is either one or zero (on or off).With hexadecimal, the digit values range from zero to fifteen, so symbols are needed to represent ten, eleven, ... fifteen as single digits. The letters A through F were chosen, so:A represents tenB = elevenC = twelveD = thirteenE = fourteenF = fifteen

You could first convert it to binary, and then to hexadecimal. Because octal and hexadecimal bases are both powers of two, the conversion between those bases and binary is quite easy. To go from octal to binary, take each digit in the number, and convert it to three binary digits: 5 -> 101 3 -> 011 2 -> 010 4 -> 100 So the binary version of the number is: 101 011 011 010 100 In order to convert to hexadecimal, your number of digits needs to be divisible by four (as 24 = 16). To get that, we need to add a digit, which will be a zero as our leftmost digit: 0101 0110 1101 0100 Now we can convert each of those sets of four binary digits into single hexadecimal digits, giving us our final answer: 9AD8

The connection between binary and hexadecimal in the programming world is exactly the same as the connection in the mathematical world. All numeric bases that are themselves a power of 2 (base-4, base-8, base-16, base-32, etc) are trivial to convert both to and from binary. A single base-4 digit maps to exactly 2 binary digits: 0 = 00 1 = 01 2 = 10 3 = 11 A single base-8 (octal) digit maps to exactly 3 binary digits: 0 = 000 1 = 001 2 = 010 3 = 011 4 = 100 5 = 101 6 = 110 7 = 111 A single base-16 (hexadecimal) digit maps to exactly 4 binary digits (also known as a nybble): 0 = 0000 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 a = 1010 b = 1011 c = 1100 d = 1101 e = 1110 f = 1111 And so on for base-32, base-64, etc. Hexadecimal is the most useful notation because a byte is normally 8 binary digits in length and we can represent a byte as two nybbles using just two hexadecimal digits as opposed to 8 binary digits. For longer binary values, such as 32-bit, 64-bit or 128-bit values, using a more concise notation makes the value much easier to read. Consider the following: 1011010010110100101101001011010010110100101101001011010010110100 1011010010110100101111001011010010110100101101001011010010110100 These two binary values look the same but they are not. With hexadecimal notation it becomes easier to see the difference because there are fewer digits to compare: b4b4b4b4b4b4b4b4 b4b4bcb4b4b4b4b4

A binary number system has two states '0' '1' for a long word in bits it can be as follows 101010101010101010101011 intimidating RIGHT? it can be represented in groups of 3 bits in octal 10/010/101/010/101/010/101/011= 22525253 digital or in group of 4 bits as 10/1010/1010/1010/1010/1010 = 2AAAAA 111 =7 octal 1111=f F in hexadecimal numbers 1000 =8 1010 =10 or A

How many bytes are there in a longword? How to turn hexadecimal CABBAGE4U into a single binary longword?

Octal (base 8) and hexadecimal (base 16) are simply shorthand notations for binary sequences. We can actually use any base that is a power of 2 (including base 4, base 32, base 64, and so on) as a shorthand for binary, but we use octal and hexadecimal because they are fairly easy to work with. If we look at base 4 first, we can better understand the relationship between binary and all other bases that are a power of 2. Base 4 only uses 4 symbols, 0, 1, 2 and 3. In binary these would be represented by 00, 01, 10 and 11 respectively. Thus a single base 4 digit can be used in place of every two binary digits, essentially halving the length of any binary sequence. Base 8 (octal) uses 8 symbols, 0, 1, 2, 3, 4, 5, 6 and 7. In binary that is 000, 001, 010, 011, 100, 101, 110 and 111. Thus a single octal digit can be used in place of every 3 binary digits, reducing the length of a binary sequence by two-thirds. Similarly, base 16 (hexadecimal) uses 16 digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e and f, and each digit can represent 4 binary digits. By the same token a single base 32 digit represents 5 binary digits, while a single base 64 digit represents 6 binary digits, and so on. Since octal notation splits a binary sequence into groups of three bits, it is ideal when the number of bits is a multiple of 3, such as in a 24-bit system. That is, a 24-bit sequence (with 24 digits), can be reduced to an octal sequence of just 8 digits. And since hexadecimal notation splits a binary sequence into groups of 4 bits, it is ideal when the number of bits is a multiple of 4, such as in a 32-bit system. Again, a 32-bit sequence (with 32 digits) can be reduced to a hexadecimal sequence of just 8 digits. We predominantly use hexadecimal as a shorthand notation for binary numbers because a byte is typically 8-bits long, thus we only need two hexadecimal digits to represent all possible values in a byte. A single hexadecimal digit therefore represents half a byte, which we affectionately call a nybble. You may well ask why we don't just use decimal notation as a shorthand for binary sequences and save us humans all the hassle of translating altogether. After all, if computers can be programmed to translate hexadecimal and octal notation into their native binary, then surely they can also be programmed to do the same for decimal. In actual fact they can and do. But when presented with a long sequence of binary such as: 01111101010011010110010011110100 it's much easier to split the sequence into groups of 4 digits and assign a single hex digit to each than it is to work out what the decimal equivalent would be. In this case the binary number splits as follows: 0111 1101 0100 1101 0110 0100 1111 0100 Then we can assign each group its hexadecimal equivalent: 7 D 4 D 6 4 F 4 Thus the hexadecimal value is 7D4D64F4. In decimal we would have to write the value 2,102,224,116 instead. While this is only 2 digits longer than the hexadecimal (if we remove the comma separators), it takes a lot longer to work it out (I cheated and used a calculator). Hexadecimal is not only a much simpler conversion (you can easily do it in your head), it also works in reverse to reveal the original binary value. Remember that we don't really care what the decimal value is -- all we're really interested in is the binary value and how we can notate it as quickly as possible using as few symbols as possible. And counting up to 16 is really not much more difficult than counting up to 10. Although it can take a bit of practice getting used to hexadecimal notation, it quickly becomes second nature, and you'll soon be counting in all sorts of bases besides base 10. You already do, in fact. The 24-hour clock is intrinsically sexagesimal, so you've been marking time in base 60 all this time (pun intended) without even realising it. The only reason it is base 60 is because it is the lowest number that is evenly divisible by 2, 3, 4, 5 and 6. The ancient Sumerians knew this 5,000 years ago. It's also the reason why circles have exactly 360 degrees.

Binary means consisting of or relating to 2, especially any kind of system that has two of something. The 'binary system' often means the numerical system that consists only of 0 and 1, as opposed to the decimal system that uses 10 digits. But there are binary stars, two stars that orbit around each other, and the word is used in many other ways as well.

A byte is a unit of measurement for binary data. A byte is somewhat useful as it contains enough data to represent characters (each character you type takes up 1 byte of storage) Bit: single digit of binary (Example: 0) Nibble: 4 digits of binary (Example: 0101) Byte: 8 Digits of Binary (Example: 01010101) Kilobyte: 1024 bytes (8192 bits) Megabyte: 1024 Kilobytes (1048576 Bytes = 8388608 bits)

There is no such thing as a binary encoded hexadecimal value. The encoding is simply the representation of a number. E.g., the symbol 42 is not a number, it is merely the representation of a number. Forty-two is an actual number. This is because 42 is only the number forty-two when the digits are base-10 (decimal). In octal notation, 42 is thirty-four and in hexadecimal notation 42 is sixty-six. Humans use decimal encoding to represent numbers simply because that's the way we were taught from an early age. We consider them easy to work with simply because we consider it easier to work in powers of 10. However, it's really no easier than working in powers of 5 or 12. Before decimalisation became the norm we actually used sexagesimal, base-60, because of its high divisibility (it's the lowest number that has all the factors 2, 3, 4, 5 and 6). Hence there are 60 seconds to the minute, 60 minutes to the hour, 24 hours in the day (2x2x2x3) and 360 degrees in a rotation. Binary and hexadecimal are simply different ways of encoding the same number. Computers only understand binary, but binary notation is tedious for humans because there are only two symbols to work with. Higher bases allow us to work with numbers more quickly because there are more symbols to play with and therefore more values we can represent with just a single digit. However, any base that is itself a power of two gives us a very simple conversion to and from binary. That is; base-4, base-8 and base-16 are more closely related to binary than is decimal. For instance, two binary digits have four possible combinations, each of which can be represented by just one base-4 digit. Three binary digits have eight possible combinations each of which can be represented by just one base-8 digit (octal notation). It therefore follows that a single base-16 digit can represent any combination of 4-bits. Since a byte is typically 8-bits in length, a hexadecimal digit is known as nybble because it is half-a-byte. Knowing this we can easily convert any number from hexadecimal to binary and back again. And if we can do it easily then a computer can do it just as easily. Converting to and from decimal is not so straightforward, but the computer can be programmed to do that for us as well, since decimal is the notation we're more used to. But when we want to instruct the computer in its own language, hexadecimal is easier to work with than decimal.

A single binary digit can represent one of two states: 1 or 0. These are often renamed as "true and false" or "on and off."

Binary (base-2) and hexadecimal (base-16) are commonly used by programmers. Binary computers only understand binary encodings. That is, all information (both instructions and data) must be converted into a numeric value; digital information. Humans like to use decimal notation whenever possible, but in order to program a computer in its own native language we must convert all values to binary, the only language the computer actually understands. However, binary is difficult to work with because there are only two symbols: 0 and 1. Decimal, on the other hand, has ten symbols, 0 to 9, so we can easily notate all values from 0 to 9 using just one digit. In binary we would need at least 4 digits to notate the same range of numbers. Thus binary numbers tend to be much longer than their decimal equivalents and are difficult for humans to comprehend; a single digit in the wrong place is much harder to spot. Although we can program the computer to convert decimal notation to native binary, this has a runtime cost because there is no direct conversion between decimal and binary notation. But base-2 is directly related to all bases that are themselves a power of 2. Thus quaternary (base-4), octal (base-8) and hexadecimal (base-16) are all directly related to binary and are therefore more easily converted back and forth than is decimal. We use hexadecimal because it has relatively few symbols (16), and each hex digit maps 1:1 with a group of 4 bits. Since 4 bits is half a byte we call hexadecimal digits nybbles. Since two nybbles make a byte, we can represent any group of 8 bits with just two symbols instead of 8 binary digits. Octal is also used because it allows us to map bits in groups of 3, which can be useful in systems that use a 9-bit byte rather than the more common 8-bit byte, but is also useful when we need to work in base-8 itself.