Using public key cryptography, X adds a digital signature σ to message M, encrypts, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations?

In a $$k$$-way set associative cache, the cache is divided into $$v$$ sets, each of which consists of $$k$$ lines. The lines of a set are placed in sequence one after another. The lines in set $$s$$ are sequenced before the lines in set $$(s+1).$$ The main memory blocks are numbered $$0$$ onwards. The main memory block numbered $$j$$ must be mapped to any one of the cache lines from

A $$RAM$$ chip has a capacity of $$1024$$ words of $$8$$ bits each $$\left( {1K \times 8} \right).$$ The number of $$2 \times 4$$ decoders with enable line needed to construct a $$16K \times 16\,\,RAM$$ from $$1K \times 8\,\,RAM$$ is

Consider an instruction pipeline with five stages without any branch prediction: Fetch Instruction $$(FI),$$ Decode Instruction $$(DI),$$ Fetch Operand $$(FO),$$ Execute Instruction $$(EI)$$ and Write Operand $$(WO).$$ The stage delays for $$FI, DI, FO, EI$$ and $$WO$$ are $$5$$ $$ns,$$ $$7$$ $$ns,$$ $$10$$ $$ns,$$ $$8$$ $$ns$$ and $$6$$ $$ns$$, respectively. There are intermediate storage buffers after each stage and the delay of each buffer is $$1$$ $$ns.$$ A program consisting of $$12$$ instructions $${{\rm I}_1},{{\rm I}_2},{{\rm I}_3},......,\,\,{{\rm I}_{12}}$$ is executed in this pipelined processor. Instruction $${{\rm I}_4}$$ is the only branch instruction and its branch target is $${{\rm I}_9}$$. If the branch is taken during the execution of this program, the time (in $$ns$$) needed to complete the program is