The first question, which Konrad Zuse discussed in 1934, was: What mathematical problems should a computing machine solve? His answer was the following definition of computing (1936): To build new specifications from given given specifications by a prescription. In the year 1943 he extended the definition to: Computing is the deviation of result specifications to any specifications by a prescription.
From these definitions Konrad Zuse defined the architecture of his computers Z1, Z2, Z3 and Z4. His computers should be free programmable, it means that they should read arbitrary instructions from a punch tape, they should work in the binary digit system because Zuse wanted to contruct his computer with binary switching elements. Not only the numbers should be represented in a binary form, but the whole logic of the machine should work in a binary switching mechanism (0-1-principle). He built a high performance floating point processor in the semi-logarithm representation, which allowed to calculated very small and very big numbers with a sufficient precison. He implemented a high performance adder with a one-step carry and a precise arithmetic exceptions handling. He developed a memory where each cell could be addressed by the punch tape and could store arbitrary data. He constructed a control unit, which controlled the whole machine, and implemented input- and output devices in the decimal number system.
His first machine, which worked on these principles, was construction from 1936-1938 (Z1). The Z1 was a machine with a 64 cell (word) memory a 32 bits and the components as discussed above. The Z1 consisted completely of metal sheets. The clock frequency was around one Hertz. The Z1 is the first programable machine of the world.
Unsatisfied with the reliability of the binary switching metal sheets he constructed the Z2. The Z2 used the mechanical memory of the Z1, but for the arithmetic and control unit he used relays (800 relays) from the phone companies. The arithmetic unit consisted of a fixed point arithmetic unit because he wanted to test the arithmetic calculations for the exponent and mantissa. The reliabilty of the relais convinced Konrad Zuse and he built the Z3 completely with relays (600 in the arithmetic unit and 2600 for the memory and control unit).
It is undisputed today, that the Z3 was the first free programmable, based on a binary floating system, working computer of the world. The Z3 did not store the program in the memory, but it contained in 1941 all the components of a modern computer as required by John von Neumann et al. in 1946.
The goal of the Z4 - developed between 1942 and 1945 - was a prototype of a series. The Worldwar 2 detroyed Konrad Zuse's hope, that his mchines should support the work of engineers.