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

Solution Step 1To Show that the binary expansion of a positive integer can be obtained by first converting positive integer into its hexadecimal equivalent and then converting each of the hexadecimal digit into four bit binary digit ( following 8-4-2-1 code)Step 2 Consider a positive Integer 56, first we need to obtain its hexadecimal equivalent. The Hexadecimal equivalent of 56 is obtained as shown below. Remainder = 8 Remainder = 3Step 3 The Hexadecimal Equivalent of 56 would be the remainders from bottom of Step-2 56 = (38)16