Multiprogramming is the act of writing programs that can be scheduled for running on more than one processor (either on a multiprocessor system, or in a clustered environment such as MOSIX). Batch-Processing is when a certain set of programs are executed, in orderly form, with the results of one program typically being fed into the following program, without any interaction from the user -- as apposed to interactive programs which requires user input at certain stages in order for the program to continue. Batch-processing can also involve the use of multiprogrammed applications, provided they can be run in a non-interactive mode.
First of all there is difference between program and a task. There may be multiple tasks running related to one program at the same time. so if the processor is busy in multiple tasks related to one program then it is multitasking. But if the multiple tasks which the processor is executing concurrently are related to different independent programs then the concept is know as multiprogramming.
Multiprogramming is collecting several jobs in a job pool and the OS selects the job from the pool so that the CPU has one job to execute , in case of any IO request for the job in execution the CPU switches to another job here switching is less compared to multitasking.So a computer system which allows such type of switching in between jobs is called a multiprogramming system. Please make note that multitasking is done by user but multiprogramming is done by operating system only.
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