Exploring 8-bit BCD and Integers: How Many Can be Represented?

[hime]

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.

 

[Mark44]

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?

 

[hime]

integers 0 to 99..so 100 integers...is this the answer?

 

[Mark44]

Yes.

 

[hime]

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?

 

[Mark44]

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.