In recent years, there has been a renewed historiographic interest in the interactions between logic and engineering practices and how they helped to shape modern computing. The focus of these writings, however, is mostly on the work of Turing and von Neumann and the question if and how their logical and mathematical works affected the shaping of the modern computer and its coding practices. For many still, the early computers are "variations on the protean design of a limited Turing machine" [31, p. 119], a perspective where the EDVAC-design, the universal Turing machine and the stored-program computer are often conflated into one single concept, hiding the complexity of earlier computers, their many differences and different histories and settings. This conflation is both historically and conceptually wrong. Rather, the Turing machine was appropriated a posteriori by computer scientists to serve as the conceptual model of a general-purpose digital computer [14], and the stored-program computer is a construction after the facts started off by IBM [22]. This demystification, however, should not distract us from the fact that logic and some of its concepts were important in the development of the digital computer, on the contrary, it should stimulate research into how these concepts were actually integrated in the practices of the rapidly developing computer field. The present paper wants to embed some important developments of the 1950s in two older traditions, one within (mathematical) logic and one within engineering. Both traditions could be termed logical minimalism, meaning the systematic use of (mathematical) logic in designing minimal systems and devices. These forms of logical minimalism were recast into a diversity of computing practices in the 40s and 50s. The logical tradition is part of the more general research programme into the foundations of mathematics and logic that was carried out in the beginning of the 20th century. The engineering tradition then emerged during the 1930s to design relay circuits and is part of a more general trend of using mathematical techniques in engineering. In the 1940s and 1950s, however, these traditions were redefined and appropriated when computer engineers, logicians and mathematicians started searching for