Beatrice Lang
Binary and hexadecimal are two different number systems. Binary is the simplest number system, using only two digits, 0 and 1, and is the basis for binary code, which is used to compose data in computers. Hexadecimal, on the other hand, has 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each hex digit represents four binary digits, so converting between the two systems involves grouping binary digits into sets of four and then converting each of these groups into a single hex digit. This article will provide a step-by-step guide on how to convert a binary number into its hexadecimal equivalent.
| Characteristics | Values |
|---|---|
| Binary number system base | 2 |
| Binary digits | 0, 1 |
| Hexadecimal number system base | 16 |
| Hexadecimal digits | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F |
| Hexadecimal digits in HTML programming for colours | 000000 (black) to FFFFFF (white) |
| First step in conversion | Write down the binary number and group the digits in sets of four |
| Second step in conversion | Multiply the 8, 4, 2 and 1's by the digit above |
| Third step in conversion | Add the products within each set of four |
| Fourth step in conversion | The digits you get from the sums in each group will give you the hexadecimal number, from left to right |
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What You'll Learn
- Binary and hexadecimal systems: Binary is base-2, uses 0 and 1, and is used in electronics. Hexadecimal is base-16 and uses 16 symbols
- Converting hex to binary: Each group of four binary digits gives you one digit in hexadecimal
- Converting binary to hex: Convert binary into another base system first, e.g. decimal
- Hex in HTML: In HTML programming, colours are represented by a 6-digit hexadecimal number. FFFFFF is white, 000000 is black
- Binary to hex conversion tools: Online tools can be used to convert binary to hex
Binary and hexadecimal systems: Binary is base-2, uses 0 and 1, and is used in electronics. Hexadecimal is base-16 and uses 16 symbols
Binary and hexadecimal are two different number systems. Binary is a base-2 numeral system, meaning it uses two symbols: 0 and 1. Each digit in a binary number counts as a power of 2. For example, the binary number 11012 is equal to 1x2^3 + 1x2^2 + 0x2^1 + 1x2^0, which equals 13 in the decimal system. Binary is commonly used in electronics.
Hexadecimal, on the other hand, is a base-16 system, using 16 symbols to represent numbers. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each digit in a hexadecimal number counts as a power of 16. For example, the hexadecimal number 62C16 is equal to 6x16^2 + 2x16^1 + 12x16^0, which equals 1580 in the decimal system.
The hexadecimal system is particularly useful in computing and digital electronics. It provides a more compact way to represent binary-coded values, making it easier to understand than long binary strings of 1s and 0s. For instance, a single hex digit can represent four digits of a binary number. This is why many computer error codes and memory addresses are presented in hexadecimal format.
To convert a binary number to its hexadecimal equivalent, you can follow these steps:
- Convert the binary number into its decimal equivalent.
- Convert the resulting decimal number into hexadecimal.
For example, let's convert the binary number 11012 into hexadecimal. Following the steps above, we first convert it into its decimal equivalent: 11012 = 1x2^3 + 1x2^2 + 0x2^1 + 1x2^0 = 1310. Now, we convert the decimal number 13 into hexadecimal. Since each digit in a hexadecimal number counts as a power of 16, we divide 1,128 by 16 to get a quotient of 70 and a remainder of 8. We then divide 70 by 16, resulting in a quotient of 4 and a remainder of 6. Finally, we divide 4 by 16, giving us a quotient of 0 and a remainder of 4. Reading the remainders in reverse order, we get 468, which is the hexadecimal equivalent of 1310. Therefore, the hexadecimal equivalent of 11012 is 46816.
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Converting hex to binary: Each group of four binary digits gives you one digit in hexadecimal
Converting hexadecimal to binary involves a two-step process: first, convert the hexadecimal number into its equivalent decimal number, and then convert the resulting decimal number into binary.
The hexadecimal number system uses 16 digits, including numbers and letters. It consists of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A, B, C, D, E, F. Each hexadecimal digit corresponds to a 4-bit binary number. So, to convert hex to binary, we need to group the binary numbers in groups of four and convert them one at a time.
For example, let's convert the hexadecimal number A2B16 into its binary equivalent. First, we need to convert A2B16 into a decimal number. A is equal to 10 in decimal, B is 11, and 16 is 16. So, A2B16 is equal to 10 x 16^2 + 11 x 16^1 + 16 x 16^0, which equals 4210 in decimal.
Now that we have the decimal equivalent, we can convert it into binary. To do this, we divide the decimal number by 16 repeatedly, writing down the remainders as hexadecimal digits. So, 42 divided by 16 is 2 with a remainder of 10. We write down the remainder, 10, which is A in hexadecimal. Now, we divide 2 by 16, which equals 0 with a remainder of 2. Writing down the remainder, we get 2. So, the binary equivalent of A2B16 is 10100010.
Another example is the hexadecimal number 4EA2. Each hexadecimal digit is replaced with its corresponding four-bit binary number. So, 4EA2 in binary is 0100 1110 1010 0010. As you can see, the binary numbers are grouped into four-bit segments, which correspond to the individual hexadecimal digits.
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Converting binary to hex: Convert binary into another base system first, e.g. decimal
To convert a binary number into hexadecimal, you can first convert the binary number into its decimal equivalent and then convert the resulting decimal number into hexadecimal.
A binary number is expressed in the base-2 numeral system, with the digits 0 and 1. Each digit of a binary number counts as a power of 2. For example, 11012 is equal to 1x2^3 + 1x2^2 + 0x2^1 + 1x2^0, which equals 1310.
A hexadecimal number, on the other hand, is expressed in the base-16 numeral system and uses 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each digit of a hexadecimal number counts as a power of 16. For example, 62C16 is equal to 6x16^2 + 2x16^1 + 12x16^0, which equals 15810.
To convert a binary number to decimal, write the binary number in reverse order. Then, create a table with columns for powers of 2, binary digits, and partial sums. In the powers of 2 column, list the powers of 2 in ascending order, starting from 2^0. In the binary digits column, write the corresponding binary digits from the reversed binary number. Finally, multiply each binary digit by its corresponding power of 2 and write the result in the partial sums column. The sum of these partial sums is the decimal equivalent of the binary number.
Once you have the decimal equivalent of the binary number, you can convert it to hexadecimal by repeatedly dividing the decimal number by 16 and writing down the remainders as the hexadecimal digits. This process continues until the quotient becomes 0. If any remainder is greater than 9, replace it with the corresponding hexadecimal letter (A = 10, B = 11, C = 12, etc.). The hexadecimal digits are then read from right to left to obtain the hexadecimal equivalent of the original binary number.
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Hex in HTML: In HTML programming, colours are represented by a 6-digit hexadecimal number. FFFFFF is white, 000000 is black
In HTML programming, colours are represented by a 6-digit hexadecimal number. Each of the 6 digits can be one of 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, or F. This is because hexadecimal numbers are expressed in base 16. Each digit represents a power of 16. For example, #FFFFFF is displayed as white because all three colour components (red, green, and blue) are set to their highest value (FF). Similarly, #000000 is displayed as black because all three colour components are set to their lowest value (00).
The hexadecimal system is convenient for representing colours because it allows for 256 (16^2) distinct values for each colour component (red, green, and blue). This means that there are 256^3 = 16,777,216 possible colours that can be represented using the hexadecimal system.
It is important to note that the order of the digits in a hexadecimal colour code matters. For example, #00FF00 is displayed as green because the digit representing green (FF) is set to its highest value, while #0000FF is displayed as blue because the digit representing blue (F) is now set to its highest value.
Sometimes, you may see a 3-digit hex code in the CSS source. This is a shorthand for some 6-digit hex codes. For example, #f0c is shorthand for #ff00cc. The 3-digit hex code can only be used when the values for red, green, and blue are the same.
To convert between hexadecimal and binary, you must first convert the hexadecimal number to its equivalent decimal number. Then, convert the decimal number to binary. For example, the hexadecimal number A2B16 can be converted to binary by first converting it to the decimal number 2604, then converting 2604 to binary (1010010101002).
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Binary to hex conversion tools: Online tools can be used to convert binary to hex
Converting binary to hexadecimal (hex) can be done using online conversion tools. These tools can be used to convert binary to hex by following a few simple steps.
The binary numeral system is a base-2 system, meaning that it uses only two numbers: 0 and 1. Each digit in a binary number is raised to the powers of 2, starting from the rightmost position with 20. For example, the binary number 11012 is equal to 1x23 + 1x22 + 0x21 + 1x20, which equals 1310.
The hexadecimal system, on the other hand, is a base-16 system. It uses 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Each hex digit represents four binary digits, so four binary digits will be equal to one hex digit. For example, the hex number 62C16 is equal to 6x162 + 2x161 + 12x160, which equals 15810.
To use an online binary-to-hex conversion tool, you first need to write down the binary number and group the digits (0s and 1s) in sets of four, starting from the right. If the leftmost group doesn't have enough digits to make a set of four, add extra 0s. Then, write 8, 4, 2, and 1 below each group as these are the weights of the positions or placeholders in the number (23, 22, 21, and 20). Finally, multiply the 8, 4, 2, and 1 by the digit above, and each group of four in binary will give you one digit in hexadecimal.
There are several online binary-to-hex conversion tools available, such as those offered by Rapid Tables and Binary Hex Converter. These tools can be used to quickly and easily convert binary numbers to their hexadecimal equivalents.
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Frequently asked questions
Converting binary to hexadecimal is easy. One hexadecimal digit is exactly four binary digits, so group your binary numbers in groups of four and convert them one at a time. For example, D matches to 1110.
The easiest way to convert binary to hexadecimal is to first convert the binary to decimal. Then, convert the decimal to hexadecimal.
To convert binary to decimal, first, write the binary number in reverse order. Then, create a table with columns for powers of 2, binary digits, and partial sums. In the powers of 2 column, list 2^0, 2^1, 2^2, and so on, going up to the highest power of 2 that is less than or equal to the length of the binary number. In the binary digits column, write the corresponding binary digits from the reversed binary number. In the partial sums column, multiply each binary digit by its corresponding power of 2 and write the result.
