Radiation-tolerant computing is of great importance to the aerospace community because future missions demand more computational power. Of special interest to the aerospace community are flight computers implemented on static random-access-memory-based field-programmable gate arrays. Such computer systems allow the in-flight reconfiguration of hardware that enables the practical deployment of truly reconfigurable computers. However, commercial static random-access-memory-based field-programmable gate arrays are uniquely susceptible to ionizing radiation. This paper introduces a computer architecture for static random-access-memory-based field-programmable gate arrays that resists failures caused by ionizing radiation. The approach extends the widely accepted fault mitigation practice of triple modular redundancy and configuration memory scrubbing by adding spare circuitry and environmental awareness through an ionizing radiation sensor. This paper describes the design of the system in addition to a theoretical analysis of its reliability using a Markov model and empirical analysis using a fault injector. A full system prototype is presented that includes a custom radiation sensor and a computer system implemented on a Xilinx Virtex-6 field-programmable gate array. Both the theoretical analysis and laboratory testing show the approach to be significantly more reliable than field-programmable-gate-array-based computers using only triple modular redundancy and scrubbing.