## Binary to Decimal Numbers, Octal, Hexadecimal

Mathcrave Binary, Octal, and Hexadecimal Number AI is a form of artificial intelligence that is used to help process and convert different numerical systems.

**About Mathcrave Binary AI Tutor**

This kind of AI tutor is used to identify numbers in the Binary, Octal, and Hexadecimal systems and is also able to convert one system to another. It is capable of extracting information from these systems and can quickly adjust to new types of numerical systems when faced with them.

Binary numbers are numbers expressed in base 2, with each place value represented by a 0 or a 1. Octal numbers are base 8, meaning each place value is a number from 0 to 7. Hexadecimal numbers are base 16, with each place value represented by numbers 0-9 and then characters A-F.

**The Problem It Solves**

- recognize a binary number
- convert binary to decimal and vice-versa
- add binary numbers
- recognize an octal number
- convert decimal to binary via octal and vice-versa
- recognize a hexadecimal number
- convert from hexadecimal to decimal and vice-versa
- convert from binary to hexadecimal and vice-versa

**Examples**

**Binary to decimal conversion**

Binary numbers are base 2 numbers, as opposed to our standard base 10 numbers. In binary, every digit can either be 0 or 1. To convert a binary number to its decimal equivalent, we must multiply each bit (binary digit) by increasing powers of 2 starting from the rightmost bit, which is the least significant bit.

For example, if we have the binary number 10011011, it can be converted to decimal as follows:

1 x 2^7 = 128

0 x 2^6 = 0

0 x 2^5 = 0

1 x 2^4 = 16

1 x 2^3 = 8

0 x 2^2 = 0

1 x 2^1 = 2

1 x 2^0 = 1

Adding all the values, we get: 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155

Therefore, **10011011** in binary is **155** in decimal.

**Important Sample Queries for Best Result**

**Conversion from any base to decimal fraction**

Sample query:* Convert 0.1011 from base 2 to a decimal fraction *

**Conversion from decimal to binary numbers **

Sample query:* Convert 0.1011 from base 2 to a decimal fraction, please show some steps *

**Binary additions**

Sample query:* Perform binary addition 1001 + 10110*

**Conversion from any base to Octal**

Sample query:* Convert 0.59375 of base 10 to octal*

**Binary to Decimal Numbers, Steps Follow:**

*1. Identify whether the binary number is an integer or a fraction.2. If the binary number is a fraction, determine the negative powers of 2 for each digit.3. Multiply each digit of the binary number by the corresponding power of 2.4. Add the results to obtain the decimal equivalent.5. If the binary number is an integer, determine the sum of positive powers of 2 for each digit.6. Add the sum to any negative powers of 2 from the fractional part, if applicable.7. Obtain the decimal equivalent by adding those results.*