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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.

a bit is a single 1 or 0 in binary

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.

That is called a "bit", short for "binary digit".

Related questions

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

Binary is a number system which only has two possible digits. That corresponds with the on and off signals in computers, where 0 means off and 1 means on. Binary digits are often used in convenient groupings. For instance, 4 binary digits (a "nybble") represent a single hexadecimal digit. Hexadecimal is a 16-base number system with digits 0 to 9, A to F, thus giving 16 possibilities. Eight binary digits, or two hexadecimal digits, is another convenient grouping called a byte. A byte represents 256 possibilities.

Hexadecimal is simply short-hand for binary numbers. Because hexadecimal is base 16 or 24 , every 4 binary bits can be expressed as a single hexadecimal character. For example, 1110 is E in hexadecimal and 1111 0011 1000 1010 is written as F38A in hexadecimal. Writing memory addresses, binary code, or IP addresses in hexadecimal results in number which has 75% less characters. The hexadecimal system uses sixteen distinct symbols, most often the symbols 0-9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen. When dealing with large values the hexadecimal system solves this problem and it is simple to convert a hex digits into a binary digits.

Binary is base-2 and hexadecimal is base-16, which is convenient because they are both powers of 2. This means that we can easily represent binary numbers using hex. For example, say we have 1 byte (8 bits) of binary data: 011010112 A single hex digit is from 0-15 (numbers above 9 are represented using A - F), which can represent 4 binary digits (2^4), so we can represent the above 8 digit binary number with 2 hex digits: 01102 = 610 = 616 10112 = 1110 = B16 Therefore 011010112 = 6B16 (also written as 0x6B) This becomes very useful when attempting to make sense of large amounts of binary data.

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

Each hexadecimal digit can hold one of 16 values (0-F); 16 = 2^4, so exactly 4 bits (binary digits) can hold the same value as 1 hexadecimal digit. As a result the conversion from binary to hexadecimal is simply a matter of grouping the bits together in blocks of 4 (making nybbles) and converting each block into a single hexadecimal digit. Similarly for binary to octal but in this case as 8 = 2³ the bits are group into blocks of 3 which are then converted into octal digits. However, converting decimal to hexadecimal is not so "easy" as each decimal digit does not map to an exact number of binary digits. The only exception would be when using BCD (Binary Coded Decimal) where only the bit patterns for the decimal digits 0-9 are used in every 4 bits (wasting 6 possible digits) and where 0000 1001 (09) + 0000 0001 (01) = 0001 0000 (10). In this case the hexadecimal representation of the BCD is exactly the same as the decimal, but I have never seen it used as such (beyond the binary representation).

4

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 nibble is half a bit octet (commonly known as a byte). A nibble, therefore, is a set of four binary digits. The numeric value of a nibble is commonly presented in binary form, or in form of a single hexadecimal digit.

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

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

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.

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