Chapter 2, Problem 50E

Explanation of Solution

Floating point model:

The floating point representation used here is 14-bit format, which is segmented into a signed bit, a 5 bits for the exponent and a 8 bit for mantissa.

To calculate:

$\begin{array}{l}\text{b+(a+c)}\\ \text{(b+a)+c}\end{array}$

Substitute $1.0\times 2^9$ for a, $-1.0\times 2^9$ for $b$ and $1.0\times 2^1$ for $c$

$\begin{array}{l}\text{b+(a+c)=b+(1}{\text{.0×2}}^{\text{9}}\text{+}{\text{.000000001×2}}^{\text{9}}\text{)}\\ \text{=b+(1}{\text{.000000001×2}}^{\text{9}}\text{)}\\ \text{=b+1}{\text{.00000000×2}}^{\text{9}}\text{(1 is discarded becuase mantissa has only 8-bits)}\\ =(-1.0{\text{×2}}^{\text{9}})+(1.0{\text{×2}}^{\text{9}})\end{array}$

$=0$

Hence, $\text{b+(a+c)=0}$

Substitute $1$