How Many Integers Can Be Represented in 8-bit BCD?

  • Thread starter Thread starter hime
  • Start date Start date
  • Tags Tags
    Bit Integers
AI Thread Summary
An 8-bit word can represent integers in binary coded decimal (BCD) format, allowing for two decimal digits. This means it can represent integers from 0 to 99, totaling 100 possible values. In a 32-bit word, BCD can represent up to 8 decimal digits, equating to 10^8 integers. While BCD is effective for decimal representation, it is considered wasteful compared to binary, as a byte can hold 256 different values in standard binary form. Overall, BCD is limited in efficiency despite its straightforward decimal representation.
hime
Messages
23
Reaction score
0

Homework Statement


Suppose a computer has 8-bit words. How many different integers can be represented (in decimal) in a single word if the integers are represented in binary coded decimal(BCD)?

Homework Equations



BCD= Binary Coded Decimal

The Attempt at a Solution


BCD is coded in 4 bits so 8bits/4bits =2 but I think its wrong..I do not know how to do this problem.
 
Physics news on Phys.org
So far, so good, but you're not done. An 8-bit word can hold two decimal digits, so how many integers can be represented in two decimal digits?
 
integers 0 to 99..so 100 integers...is this the answer?
 
so if there are 32 bits, we have 8 decimal digits if we code the integers in BCD(4bits/integer). That means, 10^8 integers(0 to 10^8-1) can be represented in BCD with 32 bits. Is this correct?
 
Yes. I should add that BCD is somewhat wasteful. As you have already found, a byte can hold two decimal digits in BCD form, so can represent 100 numbers. On the other hand, the eight bits in a byte can hold one of 256 numbers, either 0 through 255 for unsigned numbers, or -128 through 127 for signed numbers.
 
Back
Top