Let 101001 be the binary representation of a number. When converted to decimal, we obtain the number as base2dec (101001', 2)=41. When converted to octal representation, we obtain the number as dec2base (41,8)=51. We note that the last digit of octal representation (1) is the decimal representation of last 3 digits of binary representation (001), and the second last digit of octal representation (5) is the decimal representation of first 3 digits in binary representation (101) a) Prove that the following statement is ALWAYS true (note that your proof must be done for general conditions and not using the specific example): "If abcdef, is the binary representation of a number with 6 digits (which can either be 0 or 1), then the octal representation of the number is given by ryg with 2 digits where is the decimal equivalent of the first 3 binary digits "abc" and y is the decimal equivalent of the last three binary digits "def