010101 B to Ary – Easy Conversion Explained

The value of 010101 b in ary is approximately 21.3125.

Converting 010101 from binary (b) to ary involves interpreting the binary number as a base-2 value, then transforming it into a decimal, and finally into the target base, which is ary. Since 010101 in binary equals 21 in decimal, converting to ary may involve fractional parts if ary is a fraction or decimal base, but here, assuming ary is a decimal-like system, the main step is binary to decimal, then to ary.

Conversion Result

Conversion Formula

To convert binary (b) to ary, first change binary to decimal. Each binary digit is multiplied by 2 raised to the position power, starting from right to left, where the rightmost digit is position 0. Sum all these values to get decimal. Then, if ary is decimal, the value remains; if it's another base, convert accordingly.

For example, binary 010101 equals (0×2^5)+(1×2^4)+(0×2^3)+(1×2^2)+(0×2^1)+(1×2^0) = 0+16+0+4+0+1=21. So, 010101 b equals 21 in decimal, which is 21 in ary if ary is decimal.

Conversion Example

• Number: 11100
• Step 1: Binary 11100
• Step 2: Calculate decimal: (1×2^4)+(1×2^3)+(1×2^2)+(0×2^1)+(0×2^0) = 16+8+4+0+0=28
• Step 3: Convert decimal 28 to ary: as ary is decimal, result is 28

• Number: 1001
• Step 1: Binary 1001
• Step 2: Decimal: (1×2^3)+(0×2^2)+(0×2^1)+(1×2^0)=8+0+0+1=9
• Step 3: Result in ary: 9

• Number: 1010
• Step 1: Binary 1010
• Step 2: Decimal: (1×2^3)+(0×2^2)+(1×2^1)+(0×2^0)=8+0+2+0=10
• Step 3: Result in ary: 10

Conversion Chart

This chart shows binary numbers from 10076.0 to 10126.0 converted into decimal values, which are equivalent to ary values assuming decimal base. Use the table to quickly find the decimal equivalent for a binary number in this range.

Related Conversion Questions

• How do I convert binary 010101 into an integer in ary?
• What is the decimal equivalent of binary 010101 in the ary system?
• Can I convert 010101 b directly to a hexadecimal value in ary?
• What is the process to change binary 010101 to any other base?
• How do fractional parts of binary numbers convert into ary?
• Is there an easy way to convert 010101 b to fractional ary values?
• How does the conversion change if ary is a base-8 or base-16 system?

Conversion Definitions

b

"b" is a notation for binary numbers, which are expressed using only 0s and 1s, representing the base-2 numeral system used in digital computing and data processing.

ary

"ary" refers to a numerical base system, which can be any base such as decimal (10), binary (2), or hexadecimal (16). It indicates the system in which a number is expressed, often involving converting from one base to another.

Conversion FAQs

How is binary 010101 converted into decimal?

By assigning each digit a power of 2 based on its position from right to left, then summing the results. For 010101, the calculation is 0×2^5 + 1×2^4 + 0×2^3 + 1×2^2 + 0×2^1 + 1×2^0 which totals 21.

What happens if I input an invalid binary number in the conversion tool?

The script only accepts numeric inputs, so if you enter characters other than 0 or 1, it may produce incorrect results or no output. To ensure accurate conversion, only binary digits should be entered.

Can this conversion process handle fractional binary numbers?

Yes, but the process becomes more complex, involving negative powers of 2 for fractional parts. The current script handles only whole binary numbers; extending it for fractions requires additional logic.

Is the conversion from binary to ary reversible using this tool?

Yes, as long as both systems are standard bases like decimal or binary, the conversion is reversible. You can convert back and forth by applying the appropriate base change formulas.

How accurate are the results when converting large binary numbers?

The calculations are precise within JavaScript's floating point limits. For very large numbers, small rounding errors may occur; for exact conversions, specialized software or arbitrary-precision libraries are recommended.

Last Updated : 22 July, 2025

Sandeep Bhandari

Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.