Non negative integers
 

Ok I've got a practice homework question for my Hardware Design class and it states:


i dont even know where to start, can someone point me in the right direction? Any help would be appreciated

whoo... ok word size is referring to the 32 and 64 bits.
binary encoding is making a non-negative int using binary.
aka 0 = 32 0's
1 = 000....00001
etc.
BCD is binary-coded decimal. (that's the term you'll wanna google 'cuz i don't recall exactly how it's represented).
so, basically, he wants to know the range of numbers that can be encoded in 32 and 64 bits for each kind of encoding.

Well, you want to know all the different integers that can be expressed in a coding.

Binary coding should be easy. Each distinct combination of bits represents a different number. So, you've got 32 or 64 bits...how many distinct numbers can you come up with? In ASCII coding, each byte (8 bits) can represent 1 of 10 different digits. You've got 32 or 64 bits, which is 4 or 8 bytes...how many different numbers can you get?

a. is easy. ;)
b. BCD takes a base-10 number and encodes each digit with 4 bits of binary. For example the number 328 is represented by 0011 0010 1000. With 32 bits you can fit 8 BCD digits, so you can represent 10^8 or 100000000 numbers (0-99999999). 10^16 for 64-bit words.
c. Now this one is a little bit unclear. The answer varies depending on which ASCII characters you can use as digits. It also varies depending on whether you're using extended ASCII since each character is 7 bits if not and 8 bits if so. I'll assume 32-bit words and 8-bit characters for now. If you're only using the digits 0-9 for base-10, the answer is 10^4 or 10000. However, what if you're encoding hex numbers (base-16), then the answer is 16^4 because there are 16 possible digits, usually 0-9 and A-F. If you're using every ASCII character as a digit (base-256) you can represent 256^4 numbers. My guess is that you're supposed to assume you're encoding base-10.

wow thanks for the help guys

my actual homework is a lot harder than this, so hopefully i can get into some office hours to get some help