1. Data Representation Limitations
CSCE 121
J. Michael Moore

2. Limitations of Finite Data Encodings
Overflow - number is too large
suppose 1 byte stores integers in base 2
Range: 0 ( ) to 255 ( ) (note: this is not two’s complement although it would have the same problem)
if the byte holds 255 (top of the range)
adding 1 to it results in 0, not 256
J. Michael Moore

3. Limitations of Finite Data Exchange
Roundoff Error
Insufficient precision (size of word)
ex. Try to store 1/8, which is in binary, with only two bits
Nonterminating expansions in current base
ex. Try to store 1/3 in base 10, which is …
Nonterminating expansions in every base
ex. Irrational numbers such as 
J. Michael Moore

4. Limited bits There are a limited number of bits to represent a value.
Sometimes a value just cannot be represented in a finite number of bits.