1. Amdahls law states that if you speed up portions of a program eventually the parts you do not parallelize (that are sequential) will dominate the running time, and thus you reach the point of diminishing returns. Write a formula that mathematically represents this law. Consider a program in which the dynamic execution breakdown of operations (assume unit latency) is the following: 30% memory ops, 40% integer ALU ops, 13% branches, and 17% floating-point ops. What is the maximum theoretical achievable speedup (versus a sequential machine) for a VLIW machine with one branch unit (and unlimited other resources)?

2. Assuming a target VLIW machine with two memory units, four integer units, two floating-point units, and one branch unit, what is the maximum achievable speedup (versus a sequential machine) for this VLIW machine on the program described in the previous exercise?

Hint: Amdahls law says that the sequential parts of the program becomes the bottleneck since the parallel parts can be speeded up by parallel resources whereas sequential parts can not be speeded up no matter how many parallel resources are present. Amdahls law calculates the expected maximum speed-up due to parallel and sequential parts. In this problem, you will have to carefully apply the principle of Amdahls law to VLIW processors with a given number of resources as stated in each problem. Note that "unlimited resources" means you can schedule as many instructions of the same kind (e.g., add) as possible simultaneously without worrying about the number of adders available in the machine