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.