Conversion Result

The binary number 01100 b equals 12 in the ary system.

To convert 01100 from binary (base 2) to ary (base 12), first, we interpret the binary as decimal, which is 12. Since the target system is base 12, the decimal value 12 is represented as 10 in ary (since 12 divided by 12 equals 1, with 0 remainder). Therefore, 01100 b is 10 in ary.

Conversion Explanation

Converting binary to ary involves two steps: first, change binary to decimal, then convert that decimal into the ary system. Binary 01100 is calculated as (0×2^4) + (1×2^3) + (1×2^2) + (0×2^1) + (0×2^0) which equals 0 + 8 + 4 + 0 + 0 = 12. Next, convert decimal 12 to base 12: 12 divided by 12 equals 1 with 0 remaining, so the representation is 10 in ary.

Conversion Tool

Conversion Formula

To turn binary b into ary, first, convert binary to decimal by summing each digit times 2 raised to its position power. Then, divide that decimal by 12 repeatedly, recording remainders, to get the digit sequence in base 12. The process relies on positional notation and division-remainder method.

For example, binary 01100: (0×2^4)+(1×2^3)+(1×2^2)+(0×2^1)+(0×2^0) = 12 decimal. Divide 12 by 12: quotient 1, remainder 0. The digits are read from last remainder to first: 10 in ary.

Conversion Example

• Convert decimal 25 to ary:
  • Divide 25 by 12: 25/12 = 2 with a remainder of 1.
  • Divide 2 by 12: 2/12 = 0 with a remainder of 2.
  • Digits from remainders: 2 and 1, read backwards: 21 in ary.
• Convert decimal 50 to ary:
  • 50/12 = 4 with a remainder 2.
  • 4/12 = 0 with a remainder 4.
  • Digits: 4 and 2, so 42 in ary.
• Convert decimal 7 to ary:
  • 7/12 = 0 with a remainder 7.
  • Result is 7 in ary since quotient is 0.
• Convert decimal 144 to ary:
  • 144/12=12 with remainder 0.
  • 12/12=1 with remainder 0.
  • 1/12=0 with remainder 1.
  • Digits: 1,0,0, so 100 in ary.

Conversion Chart

This chart shows decimal values from 1075.0 to 1125.0 converted into ary. Use it to quickly find the ary representation for these decimal numbers.

Related Conversion Questions

• How do I convert 01100 in binary to other base systems like decimal or hexadecimal?
• What is the process to change binary 01100 to base 8 (octal)?
• Can I convert 01100 from binary directly into base 16 (hexadecimal)?
• What is the value of 01100 b in base 5, and how to do it?
• How to interpret 01100 in binary if I want to know its base 12 equivalent?
• Is there an easy way to convert binary numbers like 01100 to base 10 without a calculator?
• How do I convert binary numbers to base 12 with manual steps?

Conversion Definitions

b

The term “b” refers to binary, a base-2 numeral system using only two digits: 0 and 1. It is used in digital electronics and computing systems to represent data, with each digit representing a power of 2 depending on its position, starting from zero at the rightmost digit.

ary

The “ary” system refers to any positional numeral system with a specified base, such as base 12 (duodecimal). It uses digits from 0 up to one less than the base, with each position representing a power of that base, allowing for compact representation of numbers.

Conversion FAQs

What does it mean when binary 01100 is converted to ary?

Converting binary 01100 to ary means changing the number from base 2 to base 12, which involves interpreting the binary as decimal first and then expressing that decimal in base 12. It helps in understanding how numbers relate across different systems.

Why is the conversion from binary to ary important in computing?

This conversion helps in applications where different numbering systems are used, such as in encoding, data storage, or communication protocols, and allows for compatibility and easier interpretation of data across systems with varying bases.

Can I do the conversion manually without a calculator?

Yes, by first converting binary to decimal using positional notation, then dividing the decimal number by the target base repeatedly, recording remainders, and reading the remainders backward to get the final number in the new system.