Arithmetic Exception Handling

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Arithmetic Exception Handling

The Z3 disposed of an arithmetic exception handling. Konrad Zuse implemented the exception handling because he wanted to be sure that the Z3 calculates the numbers correctly even when the Z3 is working without a supervisor. The Z3 recognized the following operations:

Underflow of the range of numbers is: 0.
Overflow of the range of numbers is: $\infty$ .
For the calculation with 0 holds: $0+x=x$ , 0 $\bullet$ x = 0, x / 0 = $\infty$ .
For the calculation with $\infty$ holds: $x+\infty =\infty ,$ x $\bullet \infty$ = $\infty$ , 1 / $\infty$ = 0.
All operators with $?$ have the result $?$
0/0 = undefined
$\infty$ - $\infty$ = undefined
$\infty$ $\setminus$ $\infty$ = undefined
0 $\bullet$ $\infty$ = undefined

The undefined state was shown on the output device on the left side with small lights. For the numbers 0 and $\infty$ Konrad Zuse used special bit codes in the exponent. An exponent of -64 is the decimal 0. An exponent of -63 or +63 represents $\ensuremath{ą}$ $\infty$ . The Z3 calculates always correctly, if an argument is 0 or $\infty$ and the other argument is in the allowed range. The binary floating point numbers were converted to decimal floating numbers. For this conversions he needed between 9 and 41 cycles depending on the exponent. The mantissa consisted of four decimal digits (five digits for the 1) and the exponent was between -8 and +8.

Slav Petrov 2001-07-02