Non negative integers - Tilted Forum Project Discussion Community

Ace_O_Spades · 01-21-2004, 04:22 PM

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

Quote:

These days, a typical computer word is either 32 or 64 bits long. For each word size, and for each of the following encodings, determine the number of non-negative integers that can be represented:

a. Using binary encoding
b. Using BCD encoding
c. Using ASCII encoding

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

cheerios · 01-21-2004, 04:27 PM

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.

magua · 01-21-2004, 05:04 PM

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?

n0nsensical · 01-21-2004, 05:12 PM

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.

Ace_O_Spades · 01-21-2004, 06:29 PM

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

01-21-2004, 04:27 PM	#2 (permalink)
cheerios Banned Location: 'bout 2 feet from my iMac	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.

01-21-2004, 05:04 PM	#3 (permalink)
magua Tilted	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?

01-21-2004, 05:12 PM	#4 (permalink)
n0nsensical Junkie Location: San Francisco	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.

01-21-2004, 06:29 PM	#5 (permalink)
Ace_O_Spades The Death Card Location: EH!?!?	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