The 2-s complement number and DSP

More and more DSP ( digital signal processing) techniques are being used in most complex circuit designs including IC design. In general dsp requires the use of binary numbers. After all dsp is akin to a set of computations yielding a result which may or may not be converted into an analog signal. Both ways. At the input using an A/D and at the output using a D/A. In fact this is the way many recent designs in wireless are being implemented. The number system most often used is the 2-s complement number system. To refresh our memories, a 2-s complement number is formed by taking the binary representation of a decimal number, inverting the bits and then adding a "1" to it. This generates the 2-s complement. A wealth of articles exist on this in the literature and the web. The nice thing about the 2-s complement number is that addition and subtraction become very easy. An example is a dual modulus frequency divider. In this circuit we have two counters that start with a loaded number, an initial seed, and then this number is counted down. When the loaded number goes to zero a reset occurs. This is almost the very basic operation required in a dual modulus frequency divider. Note how easy the countdown becomes when implemented with 2-s complement numbers. Have the initial storage in a set of FFs, at each clock invert the contents of the FFs, use a simple adder, add 1 and at the falling edge of the clock recapture the results back into the storage FFs. Each time the clock occurs the FFs count down by '1'. Please visit the Signal Processing Group Inc., website located at http:/www.signalpro.biz for more information on our unique services, technology and technical articles. Contact us on this or other blog posts or articles as needed.