Show that the binary expansion of a positive integer can be obtained from its octal expansion by translating each octal digit into a block of three binary digits.

Solution Step 1 To Show that the binary expansion of a positive integer can be obtained by first converting positive integer into its octal equivalent and then converting each of the octal digit into 3 bit binary digit ( following 8-4-2-1 code)Step 2 Consider a positive Integer 56, first we need to obtain its octal equivalent. The Octal equivalent of 56 is obtained as shown below. Remainder = 0 Remainder = 7Step 3 The Octal Equivalent of 56 would be the remainders from bottom of Step-2 56 = (70)8