Suppose that we have four bits. a. Number 9 is represented as 10011001 in binary. Verify that the vector representation of ⌈1001⌋⌈1001⌋ is the zero vector except its 1010 th entry, which is 1.
b. Number 7 is represented as 01110111 in binary. Verify that the vector representation of ⌈0111⌋⌈0111⌋ is the zero vector except its 88 th entry, which is 1.

Required:
a. Generalize this idea for any number between 0 and 15.
b. Generalize this idea for any number of bits.