Arithmetic Algorithms: Multiplication and Division
Explore the fundamental arithmetic algorithms for multiplication and division. Understand the principles behind pipelining and how it enhances processor performance. Study hazard detection and resolution techniques.
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Arithmetic Algorithms: Multiplication and Division
Quiz • 29 Questions
Arithmetic Algorithms: Multiplication and Division - Flashcards
Flashcards • 31 Cards
Study Notes
11 min • Summary
Materials
List of Questions29 questions
- Question 1
- To act as a full adder for the incoming partial product bit.
- To shift the partial product one position to the left.
- To determine whether a multiplicand bit is added based on the multiplier bit.
- To perform the addition of the multiplicand and partial product bits.
- Question 2
- To pass the partial product vertically downward unchanged.
- To perform the AND operation between the multiplicand and multiplier bits.
- To add the multiplicand bit to the incoming partial product bit.
- To determine whether a shift operation is needed.
- Question 3
- It compensates for the delay introduced by the full adders.
- It simplifies the addition process by reducing the number of bits to be added.
- It correctly aligns the partial products for addition based on their significance.
- It ensures that the final product is properly scaled.
- Question 4
- To replace full adders for faster computation.
- To perform the shifting operation of partial products.
- To reduce the number of logic gates required.
- To handle cases where there are only two inputs to add.
- Question 5
- The longest path of input to output signal propagation through the array.
- The path with the fewest number of adders.
- The shortest path for signal propagation through the array.
- The path that determines the power consumption of the multiplier.
- Question 6
- To determine whether the multiplicand should be added to the partial product.
- To control the shifting of registers A and Q.
- To reset the flip-flop C at the end of each cycle.
- To select between the multiplier and multiplicand.
- Question 7
- To initialize the register A with zeros at the beginning of the multiplication.
- To select either 0 or the multiplicand to be added to the partial product.
- To store the carryout from the adder.
- To shift the partial product and multiplier bits.
- Question 8
- It simplifies the addition process of partial products.
- It maintains the correct sign and magnitude of the partial products.
- It ensures that the result is always positive.
- It reduces the number of bits required for the multiplication.
- Question 9
- Booth's algorithm is simpler to implement in hardware compared to array multiplication.
- Booth's algorithm is better suited for unsigned multiplication.
- Booth's algorithm always provides faster multiplication compared to other methods.
- Booth's algorithm reduces the number of addition and subtraction operations by handling blocks of 1s in the multiplier more efficiently.
- Question 10
- Perform an arithmetic right shift on the registers.
- Add the shifted multiplicand to the partial product.
- Do nothing and proceed to the next bit.
- Subtract the shifted multiplicand from the partial product.
- Question 11
- A multiplier with an equal number of 0s and 1s.
- A multiplier consisting of alternating 0s and 1s.
- A multiplier with a majority of 0s.
- A multiplier with a majority of 1s.
- Question 12
- Increasing the speed of division operations.
- Simplifying the representation of numbers.
- Reducing the number of add/subtract operations in multiplication.
- Converting multiplication into a series of addition operations.
- Question 13
- The quotient bit is set to 0 and the divisor is not added back.
- The quotient bit is set to 1 and the divisor is not added back.
- The quotient bit is set to 0 and the divisor is added back to the remainder.
- The quotient bit is set to 1 and the divisor is added back to the remainder.
- Question 14
- Shifting the divisor to the left.
- Shifting the divisor to the right.
- Taking the two's complement of the divisor.
- Inverting the divisor.
- Question 15
- It reduces the latency of a single instruction.
- It simplifies the instruction set architecture.
- It reduces the power consumption of the processor.
- It increases the throughput of instructions by overlapping their execution.
- Question 16
- Write the result.
- Fetch the instruction.
- Execute the instruction.
- Decode the instruction.
- Question 17
- To store the final result of the computation.
- To decode the instruction.
- To fetch the operands from memory.
- To temporarily hold information as it passes from one stage to the next.
- Question 18
- To receive new data with every clock pulse.
- To perform arithmetic operations such as multiplication and addition.
- To store the final result of computation.
- To control the flow of data through the pipeline.
- Question 19
- Two clock pulses.
- Three clock pulses.
- Four clock pulses.
- One clock pulse.
- Question 20
- The clock cycle time 'tp'.
- The ratio of 'tn' to 'tp'.
- The number of tasks 'n'.
- The number of segments 'k'.
- Question 21
- Overlapping the execution of current instructions with the fetch and decode of subsequent instructions.
- Executing instructions out of order to avoid stalls.
- Predicting the outcome of branch instructions.
- Using multiple ALUs to execute instructions in parallel.
- Question 22
- To process the same data stream by a cascade of processors for specific tasks.
- To simplify the instruction set architecture.
- To reduce the clock cycle time.
- To improve the performance of individual processors.
- Question 23
- Checking for overflow.
- Aligning the mantissa.
- Adding the mantissas.
- Normalizing the result.
- Question 24
- To ensure a unique representation of the floating-point number.
- To ensure that the exponents are equal.
- To make the mantissa an integer.
- To simplify the subsequent calculations.
- Question 25
- When there is a data hazard.
- When a branch instruction changes the program counter.
- When two instructions depend on the result of a previous instruction.
- When two segments try to access the same memory at the same time.
- Question 26
- Accessing memory by two segments at the same time.
- Branch instructions that change the value of the program counter.
- Instructions depending on results not yet available from previous instructions.
- Limited number of registers.
- Question 27
- An instruction attempts to read a data object before a previous instruction writes to it.
- Read after Read data dependency.
- Two instructions attempt to modify the same data object.
- An instruction attempts to modify a data object that is read by a subsequent instruction.
- Question 28
- A technique to handle interrupts.
- A method to resolve resource conflicts.
- A method to predict branch outcomes.
- A technique to bypass stalls by providing data directly to waiting instructions.
- Question 29
- Adding more registers.
- Comparing the domain and range of incoming instructions with those being processed.
- By adding more pipeline stages.
- Simplifying the instruction set.
List of Flashcards31 flashcards
- Card 1HintThink of elementary school multiplication.Memory TipShift and add to multiply.
- Card 2HintVisualize a grid of logic gates.Memory TipArray=grid.
- Card 3HintThink of the components needed for each bit.Memory TipFocus on squaring the input size.
- Card 4HintConsider delay with multiple adders.Memory TipCritical path = circuit bottleneck.
- Card 5HintConsider it as a step-by-step approach.Memory TipThink sequential, one step at a time.
- Card 6HintA 0 bit results in shift; a 1 bit results in add and shift.Memory Tip1=Add, 0=Shift.
- Card 7HintThe multiplier bit controls this operation flowMemory TipIf true, ADD it.
- Card 8HintFocus on maintaining the sign.Memory TipRemember the sign.
- Card 9HintReplicate MSB to the left.Memory TipMore bits, same sign.
- Card 10HintMSB significance.Memory Tip0 = positive, 1 = negative
- Card 11HintInvert and add 1.Memory TipTwo complements cancel.
- Card 12HintConsider overlapping bits.Memory TipName is the key.
- Card 13HintWhere do the numbers start?Memory TipClear the accumulator at start.
- Card 14HintWhat is the current and previous bit?Memory TipCompare and act.
- Card 15HintMaintain the sign bit.Memory TipKeep sign during shifting.
- Card 16HintApplicable for any sign.Memory TipHandle any sign.
- Card 17HintWhat's good about it?
- Card 18HintSign changes determine action.Memory TipMove and multiply.
- Card 19HintSkipping leads to faster.Memory TipSkip 1s for efficiency
- Card 20HintRevert to previous value if needed.Memory TipIf negative, restore.
- Card 21HintWhere are the results stored?Memory TipA and Q post division.
- Card 22HintBinary long division method.Memory TipDivide and potentially restore.
- Card 23HintA sequence of instructions being executed simultaneouslyMemory TipMany operations happening at once.
- Card 24HintRead, Decode, Perform, Write.Memory TipRDPW
- Card 25HintFocus on number crunching.Memory TipMath in segments.
- Card 26HintWorking on multiple instructions at a time.Memory TipInstructions overlap always.
- Card 27HintChain of processors.Memory TipProcessors in series
- Card 28HintOperands.Memory TipDecimal fraction pipelines
- Card 29Hint4 key processes.Memory TipCAAN=compare, align, add, normalize
- Card 30HintToo BIG.Memory TipExceeds limit.
- Card 31HintToo SMALL.Memory TipSmaller than the limit