An essential skill in computer science is the ability to understand the different interpretations of 8-bit, 16-bit, 32-bit, and 64-bit long strings of binary digits (0's and 1's), since all computing control decisions and data processing operations involve such constructs.
The ability to convert between binary and decimal representations of integers and reals, without digital or mechanical assistance, is a required skill. In fact, memorizing as many powers of 2 as you can never hurts. Neither does learning the binary and decimal values of 1K, 1M, 1G, and 1T.
Unless the problem requires a specific base, please feel free to work in powers of 2, 8, 10, or 16, for MY convenience. Whatever makes you more comfortable. Why? Because no calculators will be permitted on exams. If it excites you to use one when you work problems , or to check your homework, be my guest. However, you will be required to have mastered these conversions your self and to demonstrate such ability. So, showing your work will help you receive credit for knowing what to do, even if the numbers don't quite dance correctly below your writing implement.
Unless otherwise stated, the rightmost bit is also the
the least significant bit,
corresponding to the value in the 
position in
the base-2 interpretation of the number. And, since I
can't count anyway, for long strings of 0's and 1's, your
grouping of digits into "fours" is fine, as is using octal (base 8) or
hex (base 16). Again, this is allowed for your personal work as long as you
get the requested format for your answer.
For example, the 32-bit binary string
(11110000111101011010111100001111)
is much easier for me to read in any of the following forms:
(11 110 000 111 101 011 010 111 100 001 111) (base 2) (36 075 327 617) (base 8)
(1111 0000 1111 0101 1010 1111 0000 1111) (base 2) (F0F5 AF0F) (base 16 or H)Add this to the rules and regs for the rest of the semester, and keep in mind in doing labs and in taking exams. Oh, by the way, absolutely no calculators for exams. No exceptions.