There is a simple pattern for determining if a binary number is odd. what is it and why does this pattern occur

The answer to this question would be the least number (right most number). If the last digit of a binary number is 1, the number is odd; if it’s 0, the number is even.  If you add an even number with even number, the result should be even. But if there is just one odd number added, it will be odd. In binary, all the number is multiplied by 2x. It is pretty clear that all the number should be even beside the first/lowest multiplier   which has potential to be 1.  Everything about the binary number system is the same as the decimal number system with just one difference: the base is 2 instead of 10.

Further Explanation:-

Binary number system

Binary means base 2(note the prefix bi). Base 2 (binary) has 2 digits: 0, 1. since binary numbers are made up of binary digits, we often call a binary digit a bit (short for binary digit). We may also refer to a place value position as a bit. In other words, the binary number '1010' requires 4 bits to write, and those bits are '1', '0', '1' and '0'.For any number system that has a base b, the first b non-negative numbers are represented by the digits themselves. For base b=2 (binary), the first 2 numbers are 0 and 1.Counting in binary is just like counting in decimal, except that you run out of digits much more quickly and have to resort to more value places sooner. To count the number of eggs in a dozen in binary would be as follows: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100.  

Example:  

1101 represents an odd number (13); 10010 represents an even number (18).  To convert a binary number to base 2k , split it into groups of k digits (adding leading 0s if necessary), then convert each group to base 2k . Ex: Convert the number 1001011111 to base 8. First, note that 8 = 23 , so we should split the number into groups of 3 digits: 001 001 011 111 Note that we added two leading 0s to make the number of digits a multiple of 3. Next, we convert each group of 3 digits to base 8: 001 001 011 111 1 1 3 7 Thus, the number in base 8 is 1137.

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Keywords:  binary, number system, decimal, conversion, even binary number, odd binary.