Z3 (computer)

• 1. Introduction

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  The Z3 was the world's first working programmable, fully automatic digital computer, and it was built in secret in wartime Berlin by a single engineer named Konrad Zuse. It weighed about a tonne, consumed around 4,000 watts of power, and ran at a clock frequency of just 5-10 hertz. It could multiply two numbers in about 3 seconds. Today, a smartphone does billions of such operations every second. Yet this hulking, relay-driven machine, completed in 1941, established principles that every computer on the planet still follows. How did one man, working largely without government support and often against official indifference, build the machine that invented the age of computing? And why did that machine vanish in a cloud of rubble on the 21st of December 1943?

• 2. From Z1 to Z3

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  Zuse designed the Z1 between 1935 and 1936 and spent the following two years building it. The Z1 was wholly mechanical, and it only worked for a few minutes at a time at most. That unreliability forced a rethink. Helmut Schreyer, a doctoral student at the Technische Hochschule in Charlottenburg, advised Zuse to explore vacuum tubes instead of mechanical parts. In 1937, Schreyer was already working on implementing Boolean operations and flip-flops using tubes. When he demonstrated a circuit to a small audience in 1938 and proposed an electronic computing machine, the reaction was cool. The largest operational electronic devices of the era used far fewer tubes than such a machine would require, and experts at the Telecommunication Institute considered the whole idea practically infeasible. Zuse later recalled the attitude plainly: "They smiled at us in 1939, when we wanted to build electronic machines." In 1940, Zuse and Schreyer arranged a meeting at the Oberkommando der Wehrmacht to pitch an electronic computer project. When they estimated the work would take two or three years, the proposal was rejected outright. Zuse pivoted. He decided the next design would use relays rather than tubes. A manufacturer of small calculating machines named Kurt Pannke provided financial help, and the Z2 was completed and presented to the Deutsche Versuchsanstalt für Luftfahrt in 1940 in Berlin-Adlershof. Zuse later admitted he was lucky: the Z2 actually worked that day, one of the few times it did, and that demonstration convinced the German Laboratory for Aviation to partially fund what came next.

• 3. A Machine Built in Secret

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  In 1941, working under a highly secret government project, Zuse completed the Z3. It was built with around 2,600 relays and used a 22-bit word length. Joseph Jennissen, born in 1905, served as the government supervisor from the Reich Air Ministry's Research-Leadership division, monitoring orders placed with Zuse's company, ZUSE Apparatebau. The aerodynamicist Herbert A. Wagner acted as a further intermediary between Zuse and the ministry. On the 12th of May 1941, the Z3 was formally presented to an audience of scientists, including professors Alfred Teichmann and Curt Schmieden from the Deutsche Versuchsanstalt für Luftfahrt in Berlin. Unlike the Z1, the Z3 handled floating-point arithmetic with exception handling built from just a few relays. It could generate and pass through exceptional values: plus infinity, minus infinity, and undefined quantities. It also added a square root instruction, a capability absent from its predecessors. Practical work followed almost immediately. Based on research by the German aerodynamics engineer Hans Georg Küssner, known for the Küssner effect, a program was written specifically to solve wing flutter problems. It was called "Program to Compute a Complex Matrix," and it gave the Z3 a real engineering job to do. The machine stored all its programs on punched film rather than requiring the user to rewire hardware for every new task. That was a genuine conceptual leap: change the tape, change the program. Yet the Z3 was never put into everyday operation. The government did not consider it vital, and Zuse's request for funding to replace the relays with fully electronic switches was denied. The war ministry deemed such development "not war-important."

• 4. How It Thought

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  The Z3 operated as a stack machine built around two registers, R1 and R2. A program's first load instruction pulled a value from memory into R1; the second load filled R2. Arithmetic instructions then operated on both registers, leaving the result in R1 and clearing R2. A store instruction saved R1's contents to memory and cleared R1, preparing the machine for the next cycle. Input came from a keyboard that fed numbers directly into R1. Output was displayed through a row of lamps. The data memory held 64 words of 22 bits each, and program memory lived on punched celluloid tape. An addition took about 0.8 seconds; a multiplication took about 3 seconds. What the Z3 lacked was conditional branching. It could not look at a result and choose between two different paths forward. This meant it was not equivalent to modern computers in the way it was actually programmed, as the computer scientist Raúl Rojas would later note. However, the absence of conditional branching did not prevent Zuse from building a genuinely useful machine. His main goal at the time was a workable device for engineering applications, and the Z3's instruction set served that purpose well given the hardware limits of the 1940s. The machine could construct loops, and its arithmetic capabilities were sophisticated enough to handle the kind of matrix calculations that aeronautical engineers needed.

• 5. Turing Completeness, Belatedly

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  In 1998, more than half a century after the Z3's debut, the computer scientist Raúl Rojas demonstrated that the machine was, in principle, Turing-complete. The argument was elegant and a little strange. Because the Z3 had no conditional branch instruction, any program that needed branching would have to compute every possible outcome of every branch simultaneously. The tape would need to be long enough to execute every possible path. Unneeded results would simply be canceled out, a form of speculative execution built from necessity rather than design. Rojas put the conclusion directly: "We can therefore say that, from an abstract theoretical perspective, the computing model of the Z3 is equivalent to the computing model of today's computers." He was equally direct about the practical limits: in the way the Z3 was actually programmed and used, it was not equivalent to modern computers. The theoretical proof nonetheless mattered. It placed the Z3 in the same abstract class as every general-purpose computer that followed it. Zuse had arrived at this destination not by designing toward Turing-completeness but by solving the immediate engineering problems in front of him, and the theoretical equivalence was only confirmed decades after the machine had been destroyed.

• 6. Destruction and Legacy

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  The original Z3 was destroyed on the 21st of December 1943 during an Allied bombardment of Berlin. The machine had originally been called V3, short for Versuchsmodell 3 or Experimental Model 3, but had been renamed to avoid confusion with Germany's V-weapons program. Zuse did not stop. He moved on to the Z4, completing it in a bunker in the Harz mountains, a facility he shared with Wernher von Braun's ballistic missile development. When the war ended, Zuse retreated to Hinterstein in the Alps with the Z4 in tow, where he remained for several years. In 1961, Zuse's own company, Zuse KG, built a fully functioning replica of the Z3. That replica is now on permanent display at the Deutsches Museum in Munich. A second reconstruction, directed by Raúl Rojas and Horst Zuse, ran from 1997 to 2003. The rebuilt machine is housed in the Konrad Zuse Museum in Hünfeld, Germany, where memory was halved to 32 words, power consumption dropped to about 400 watts, and weight fell to about 30 kilograms. Horst Zuse began a further reconstruction of the Z3 in 2008, presenting it at the Konrad Zuse Museum in Hünfeld in 2010. The binary system underpinning all of this work traces back to Gottfried Leibniz roughly three centuries before Zuse's time. George Boole used it to develop Boolean algebra, and in 1937 Claude Shannon mapped Boolean algebra onto electronic relays in a seminal paper on digital circuit design. Zuse developed that same groundwork independently, without knowledge of Shannon's work, as he designed and built the Z1 from 1935 to 1938. The parallel discovery became one of computing history's quieter ironies, and it is part of why Zuse has often been suggested as the inventor of the computer. Schreyer's own electronic experimental model, built using 100 vacuum tubes in 1942, was lost at the end of the war, taking one more thread of early computing history with it.