Why is a SHA-1 Hash 40 characters long if it is only 160 bit?

Question

The title of the question says it all. I have been researching SHA-1 and most places I see it being 40 Hex Characters long which to me is 640bit. Could it not be represented just as well with only 10 hex characters 160bit = 20byte. And one hex character can represent 2 byte right? Why is it twice as long as it needs to be? What am I missing in my understanding.

And couldn't an SHA-1 be even just 5 or less characters if using Base32 or Base36 ?

Answer 1

One hex character can only represent 16 different values, i.e. 4 bits. (16 = 2⁴)

40 × 4 = 160.

---

And no, you need much more than 5 characters in base-36.

There are totally 2¹⁶⁰ different SHA-1 hashes.

2¹⁶⁰ = 16⁴⁰, so this is another reason why we need 40 hex digits.

But 2¹⁶⁰ = 36^{160 log₃₆2} = 36^30.9482..., so you still need 31 characters using base-36.