Next: Clocked Maschine / Clock
Up: Konrad Zuses Z3 in
Previous: Arithmetic Unit and Carry
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: .
- For the calculation with 0 holds: , 0 x = 0, x /
0 = .
- For the calculation with holds:
x
=
, 1 / = 0.
- All operators with have the result
- 0/0 = undefined
- - = undefined
- = undefined
- 0 = undefined
The undefined state was shown on the output device on the left side with small
lights. For the numbers 0 and Konrad Zuse used special bit codes
in the exponent. An exponent of -64 is the decimal 0. An exponent of -63 or
+63 represents
. The Z3 calculates always correctly,
if an argument is 0 or 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