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Why do we need Registers?
If tcpu is cycle time of CPU which is the time taken by CPU to execute a well-defined micro-operation employing registers and tmem is memory cycle time which is the speed at which memory can be accessed by CPU then (tcpu/tmem) is in the range of 2 to 10 i.e. CPU is 2 - 10 times faster than memory. So CPU registersare the fastest temporary storage areas. So the instructions whose operands are stored in fast CPU registers can be executed fast in comparison to instructions whose operands are in main memory of a computer. Every instruction should designate the registers it will address. So a machine needs a large number of registers.
Figure: CPU with general register organisation
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calculate dy/dx if y=[x-cos(1/cos(xe/2x))]/x
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