Chapter 18, Problem 33E

Explanation of Solution

Underflow error:

Underflow error is an error which occurs when the precision digits produced by the arithmetic calculation is too small  than the allocated digits to represent in the machine.

Example: consider the following equation:

$\text{(A+B)}$        (1)

Substitute the value of $\text{A = 5688}\times {\text{10}}^{\text{-7}}$  and $\text{B = 5689}\times {\text{10}}^{\text{-7}}$ in Equation (1).

Compute the sum of the first two values $\left(\text{A+B}\right)$,

  $\begin{array}{l}5688\times {10}^{-7}\\ \underset{\_}{5689\times {10}^{-7}}\\ 11377\times {10}^{-14}\end{array}$

Here, the value $\text{11377}\times {\text{10}}^{\text{-14}}$ can be written as $\text{1137}\times {\text{10}}^{\text{-13}}$.

• The result of (A+B) is $\text{1137}\times {\text{10}}^{\text{-13}}$, which is too small to represent in the machine because the minimum exponent value that can be represented is $\text{-9}$ and the value lesser than the exponent -9 is considered as 0.
• So, logically the result of A + B is set to 0. This type of error is called underflow error