1. CEN200 Number systems DR. HAIKEL HICHRI

2. Gray codes  As we count up or down using binary codes, the number of bits that change from one binary value to the next varies.  As we count from 000 up to 111 and “roll over” to 000, the number of bits that change between the binary values ranges from 1 to 3.  For many applications, multiple bit changes as the circuit counts is not a problem. There are applications, however, in which a change of more than one bit when counting up or down can cause serious problems.

3. Gray codes  One such problem is illustrated by an optical shaft- angle encoder shown in Figure.  The encoder is a disk attached to a rotating shaft for measurement of the rotational position of the shaft.  The disk contains areas that are clear for binary 1 and opaque for binary 0. An illumination source is placed on one side of the disk, and optical sensors, one for each of the bits to be encoded, are placed on the other side of the disk.  When a clear region lies between the source and a sensor, the sensor responds to the light with a binary 1 output. When an opaque region lies between the source and the sensor, the sensor responds to the dark with a binary 0. Consider the situation when the sensor is in the boundary between 011 and 100

4. Gray codes  As a solution, we use gray code: