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An 8087 co-processor is a mathematical coprocessor designed for processing data that requires more computing horsepower than what a CPU can provide. It was introduced in 1979 as an alternative to costly, high-speed parallel computing machines. The 8087 was the first floating-point coprocessor for the IBM PC and was specifically designed to work with the IBM PC\'s 8088 microprocessor. The chip was eventually found in many other computers as well, including the Apple IIe, Macintosh SE and DOS compatible system.

The primary advantage of the 8087 co-processor is its ability to carry out highly intensive computations quickly and efficiently. It does this by taking the burden of the computation off from the CPU. This in turn allows the CPU to be used for other tasks while the 8087 handles the intensive calculations. The 8087 also has the ability to carry out calculations in floating-point format; meaning that very large (or very small) numbers can be handled with high precision.

The 8087 uses a set of instructions called the 8087 instruction set, which are an extension of the CPU\'s instruction set. The instructions are specifically designed for numerical calculations, and allow for basic mathematical operations such as addition, subtraction, multiplication, division, and square root calculations. The 8087 chip also includes anon-chip cache memory which allows it to store intermediate calculations or frequently used data, allowing for quicker retrieval of the stored data.

The 8087 is used in a wide variety of applications, ranging from numeric analysis, to complex user interfaces, to numerical simulation. It is used extensively in scientific, engineering, and mathematical applications where accuracy and speed are of the utmost importance. The chip is also used in the graphics industry, where it assists with the calculation of lighting and shading for 3D animation scenes, and in the medical industry, where it is used to perform analysis of patient data.

The working principle of the 8087 is quite simple. The instructions from the CPU are passed to the 8087, which then performs the requested calculation by utilizing its on-chip cache memory, as well as its instructions set. The result of the computation is then sent back to the CPU where it is used to either perform an action, or is stored for later use. This process is repeated until the computation is complete.

The 8087 co-processor has played an important role in the computing industry, as it has allowed for faster and more accurate computation than what was previously possible with only a CPU. With its on-chip cache memory, and its efficient floating-point calculation abilities, it has become an invaluable addition to both scientific and medical applications.