Thus, users can imagine that over time the magenta arrow jumps by 10 (the FTW) in a counter-clockwise direction on each cycle of the system clock. As a result, theta increases by ten 64ths of a circle each time until the accumulator finally rolls over at the 0 mark. Note that theta grows at a constant rate: ten 64ths of a circle per system clock cycle, thereby establishing the average roll over rate of the accumulator. In addition, the graphic on this slide shows how each accumulator value corresponds directly to an angle, theta. That is, theta equals 2-pi times x over 2^N radians, where x is the value of the accumulator at any given instant. To convert the accumulator values to sinusoidal values ADI makes use of the red scale below the phase wheel and the blue scale left of the phase wheel. The red scale represents the cosine output of the angle to amplitude converter, while the blue scale represents the sine output of the angle to amplitude converter. Both scales span the diameter of the phase wheel with the radius of the phase wheel corresponding to the peak amplitude of a D-bit sinusoid (that is, 2 raised to the D minus 1 power minus 1 for a DDS). In this example, on the kth cycle of the system clock, the accumulator has a value of 19. This identifies a particular angle and corresponds to the appropriate sine and cosine conversions as shown on the red and blue scales. One system clock cycle later, the accumulator has a value of 29 (assuming an FTW of 10), which identifies a new angle corresponding to new sine and cosine conversions. The change in the sine and cosine values is shown as a heavy blue or red arrow accordingly. As the magenta arrow continues to jump around the phase wheel by increments of 10, the corresponding sine and cosine values will map out sampled sine and cosine waveforms, respectively.