Key, plaintext block and ciphertext block permutations question

Question

Question: If a cipher’s key size is $k$ bits and its block size is $b$ bits, how many possible keys are there, how many possible plaintext blocks are there, and how many possible ciphertext blocks are there?

Studying for an exam and this popped up in a past paper without an answer, is the solution e.g. for key size $2^k$ bits? and similarly for the others will be $2^b$ bits? My friend thinks its $b^k$ so were unsure and clearly don't understand the logic behind it.

Answer 1

The answers very are very easy if you know about binary representations.

$k$-bit means the binary representation contains $k$ binary digits.

xx......xx : k binary digits

For each position can be 0 and 1 so, a $k$-bit can take $2^k$ distinct values.

You can similarly argue for $b$-bit block size, if you know that block size is the input size for block ciphers.

Since block-ciphers are keyed permutations the input space equal to output space.