A direct digital synthesis is provided with added circuitry to reduce jitter in an IC so that a programmable frequency output can be provided near the limits of the IC system clock with minimal jitter. The system derives the quotient Q as a remainder R in an accumulator at the instant of an overflow, divided by a programmable input N. The quotient Q is subjected to conversion logic that can be provided by a fast parallel to serial converter such as, for example a multi-gigabit transceiver (MGT) of an FPGA. As an alternative to an MGT, a series of delay devices such as found in a carry chain can be used if calibration is performed to assure the accuracy of delays.