Binary to Decimal to Hexadecimal Converter

Ultimate Binary to Decimal to Hexadecimal Converter. The binary-hexadecimal-decimal converter is capable of instantly converting back and forth between binary, decimal, and hexadecimal numbers.

How to use the Binary-Decimal-Hexadecimal Converter?

Our Bin-to-Dec-to-Hex converter is a very easy-to-use online tool that will enable you to perform a conversion of any binary, decimal, or hexadecimal number quickly. You can enter a number in any field and the conversion is immediate. So for example, if you start to write a binary number in the binary number field, you can see the result of the decimal and hexadecimal conversion in real-time.  Our free tool can perform the following operations:

• Binary to Decimal Conversion (as a Bin to Dec Converter)
• Binary to Hexadecimal Conversion (as a Bin to Hex Converter)
• Decimal to Binary Conversion (as a Dec to Bin Converter)
• Decimal to Hexadecimal Conversion (as a Dec to Hex Converter)
• Hexadecimal to Decimal Conversion (as a Hex to Dec Converter)
• Hexadecimal to Binary Conversion (as a Hex to Bin Converter)

Binary, Decimal, Hexadecimal numbers

What does binary number mean?

The binary number system is a numerical system where digits consist only of 1 and 0. Binary numbers are mainly used in computer science, this is the native language of computers because it describes the state of a bit, a logical value.

What is a decimal?

The decimal numeral system is the standard system for denoting integer and non-integer numbers. A decimal numeral refers generally to the notation of a number in the decimal numeral system. For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign “−”. The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot “.” in many countries, but also a comma “,” in other countries.

What does a hexadecimal number mean?

Hexadecimal refers to the base-16 number system, that represents numbers using a radix (base) of 16. The numerals 0–9 are used to represent their usual values and the letters A–F (or a–f) represent the values 10–15. For example, the decimal number 13 is represented as D (or d) in the hexadecimal numbering system.

Hexadecimal numerals are widely used by computer system designers and programmers as they can represent every byte (8 bits) as two consecutive hexadecimal digits. In this way, hexadecimal numerals provide a human-friendly representation of binary-coded values.

Binary to/from Decimal to/from Hexadecimal Conversion

How can I convert from Binary to Decimal?

In the binary system, each digit represents an increasing power of 2, with therightmost digit representing 20, the next representing 21, then 22, and so on.The value of a binary number is the sum of the powers of 2 represented by each“1” digit.

Forexample:

11001=1·2⁴ + 1·2³ + 0·2² + 0·2¹ + 1·2⁰=16 + 8 + 0 + 0 + 1=25

How do I convert a Binary number to a Hexadecimal number?

Fortunately, binary decimal conversion is very simple. All you need to do is divide the binary format number into blocks of 4 and convert them one by one. For example, conversions of 10101111 can be solved in two steps. 1010 represents 10 in the decimal and A in hexadecimal. The number 1111 represents 15 in the decimal system, so F in the hexadecimal systems. So the previous binary number is AF in hexadecimal.

How can I convert from decimal to binary?

To convert from decimal to its binary, the number is divided by two. The remainder is the least-significant bit. The quotient is again divided by two; its remainder becomes the next least significant bit. This process repeats until a quotient of one is reached. The sequence of remainders (including the final quotient of one) forms the binary value, as each remainder must be either zero or one when dividing by two.

How to convert from decimal to hexadecimal (or dec to hex)?

There are several algorithms that you can use for hex to dec conversion. The algorithm below is a simple one for converting a representation of a number to hexadecimal by doing integer division and remainder operations in the source base.

1. Divide the number by 16.
2. Get the integer quotient for the next iteration.
3. Get the remainder for the hexadecimal digit (0-9 and a-f).
4. Repeat the steps above until the quotient is equal to 0.

Let’s say we have the decimal number 195. Here is how you can use the algorithm shown above.

• 195 / 16 -> quotient=12, reminder is 3 (which is also 3 in hexadecimal).
• 12 / 17 -> quotient=0, reminder is 12 (which is ‘C’ in hexadecimal).
• So 195₁₀=C3₁₆

How do I convert a hexadecimal number to a binary number?

The operation is relatively simple, due to the fact that 16 can also be described as the power of 2. All we have to do is to rewrite the digits of the number. For example, the hexadecimal value ‘1F’ can be easily converted by converting the digits to the binary system while maintaining the local value like this:  0001 (1) and 1111 (F) – 00011111.

How to convert hexadecimal to decimal (or hex to dec)?

One of the most well-known formulas for converting a hexadecimal number to decimal is the “Division-remainder in source base” algorithm. This is a simple algorithm for converting a representation of a number to hexadecimal by doing integer division and remainder operations in the source base. In theory, this is possible from any base, but for most humans only decimal, and for most computers only binary can be easily handled with this method.

Let d be the number to represent in hexadecimal, and the series h_ih_i−1…h₂h₁ be the hexadecimal digits representing the number.

1. i ← 1
2. h_i ← d mod 16
3. d ← (d − h_i) / 16
4. If d=0 (return series h_i) else increment i and go to step 2

“16” may be replaced with any other base that may be desired.

The bin-to-dex-to-hex conversion routine is based on Gabu Siddharth’s excellent work.