Base conversion - the LOGIC and INTUITION behind it

In summary, when converting a number from base 10 to base 2, a systematic approach is to divide the number by 2's successively and keep track of the remainder. The remainder coefficients represent the binary number. The idea behind this method is not clear, but further explanation can be found in a forum discussion linked. It is possible to represent any number using any base, for example, converting 7 to base 8.
  • #1
O.J.
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Base conversion -- the LOGIC and INTUITION behind it...

for example, converting from base 10 to 2, a systematic way is to divide the number by 2's successively and keep track of the remainder. the remainder coefficients represent the binary number. Now why does this work is beyond me but I would love to know the idea behind it?

second, I am a bit unsure that you can represent each number using any base. e.g. write 7 to base 8?
 
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  • #3
forget my 2nd question. Explain to me the logic on the systematic way of converting from decimal to binary (& other bases in general), please.
 

FAQ: Base conversion - the LOGIC and INTUITION behind it

How does base conversion work?

Base conversion involves converting a number from one numerical base to another. This is done by dividing the original number by the base you want to convert it to and recording the remainder. This process is repeated until the original number becomes 0. The remainders are then read from bottom to top to get the converted number.

Why is base conversion important?

Base conversion is important in computer science and mathematics because different numerical bases have different uses and applications. For example, binary (base 2) is used in computer systems, while decimal (base 10) is used in everyday calculations. Being able to convert between bases allows for more efficient problem-solving and understanding of different number systems.

What is the difference between base 2 and base 10?

The main difference between base 2 and base 10 is the number of digits used. Base 2, also known as binary, uses only two digits (0 and 1) to represent numbers, while base 10, also known as decimal, uses ten digits (0-9). In binary, each digit represents a power of 2, while in decimal, each digit represents a power of 10.

How do I convert a number from base 10 to another base?

To convert a number from base 10 to another base, you can use the repeated division method described above. Another method is to use the base conversion formula, which involves multiplying the number by the base you want to convert it to and adding the remainders until the original number becomes 0.

What is the significance of hexadecimal in computer systems?

Hexadecimal, also known as base 16, is commonly used in computer systems because it can represent a large range of numbers in a compact and easily readable format. It is also convenient for representing binary numbers, as each hexadecimal digit corresponds to four binary digits. This makes it useful for tasks such as memory addressing and file formatting.

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