This paper describes the design and implementation of a real-time delay-and-sum synthetic aperture beamformer. The beamforming delays and apodization coefficients are described parametrically. The image is viewed as a set of independent lines that are defined in 3D by their origin, direction, and inter-sample distance. The delay calculation is recursive and inspired by the coordinate rotation digital computer (CORDIC) algorithm. Only 3 parameters per channel and line are needed for their generation. The calculation of apodization coefficients is based on a piece- wise linear approximation. The implementation of the beamformer is optimized with respect to the architecture of a novel synthetic aperture real-time ultrasound scanner (SARUS), in which 4 channels are processed by the same set of field-programmable gate arrays (FPGA). In synthetic transmit aperture imaging, low-resolution images are formed after every emission. Summing all low-resolution images produces a perfectly focused high-resolution image. The design of the beamformer is modular, and a single beamformation unit can produce 4600 low-resolution images per second, each consisting of 32 lines and 1024 complex samples per line. In its present incarnation, 3 such modules fit in a single device. The summation of low-resolution images is performed internally in the FPGA to reduce the required bandwidth. The delays are calculated with a precision of 1/16th of a sample, and the apodization coefficients with 7-bit precision. The accumulation of low-resolution images is performed with 24-bit precision. The level of the side- and grating lobes, introduced by the use of integer numbers in the calculations and truncation of intermediate results, is below -86 dB from the peak.