Harnessing quantum randomness for the generation of random numbers is an important concept crucial for information security and many other computer-related applications. Quantum random number generators (QRNGs) are evolving from bulky, slow, and expensive implementations towards chip-sized devices. Since computers are deterministic devices, and as such incapable of generating randomness, the prevailing modus operandi is that a QRNG is added to a computer, realizing what is known as "probabilistic Turing machine". State-of-the-art QRNGs use different hardware ports (USB, PCIe,...) and manufacturer-specific bit-transfer protocols, which limits their use by both hardware and software developers. In this work we propose an entirely different approach to use of randomness in a general digital environment (computers included), via a new, dedicated logic circuit: the random flip-flop (RFF), which is fully inter-operable with the standard logic circuits and can form an integral part of microprocessors, ultimately as an instruction-set extension. RFFs can be regarded as the missing link that closes the full set of logic elements; we show their use in digital and analog applications. We also build an RFF on a silicon chip using CMOS process. That, in principle, allows having any number of RFFs on a particular chip (e.g. microprocessor, FPGA, ASIC, ...), enabling both a very fast and massively parallel random number generation. Applications are endless, including recent trends in artificial intelligence, biomimetic stochastic computer and graphics processors. Integrated RFF does not need hardware ports nor bit-transfer protocols and allows an easy integration of randomness into higher programming languages.