COMPUTER ARCHICTURE AND ORGINATION
UNIT 5 ARATHMETIC
SHORT NOTES
COVERED TOPICES:- Accessing I/O Devices, Interrupts, Enabling and Disabling Inerrupts, Handling Multiple Devices, DMA,I/O Hardware, Standard I/O Interfaces:SCSI
Q.2 Explain Booth's Algorithm with Suitable Example
Booth's algorithm is a technique used for multiplying signed binary numbers efficiently. It reduces the number of partial products that need to be added together in the multiplication process. Here's how it works:
Consider two signed binary numbers A and B, where A is the multiplicand and B is the multiplier. Booth's algorithm proceeds as follows:
- Initialize two variables: the product P, initially set to 0, and the previous bit P_prev, initially set to 0.
- Repeat the following steps until all bits of the multiplier B are processed:
- Check the current bit of B and the previous bit P_prev.
- If the current bit of B is 1 and the previous bit P_prev is 0, add A to P.
- If the current bit of B is 0 and the previous bit P_prev is 1, subtract A from P.
- Shift A and P right by one bit.
- Update P_prev to the current bit of B.
- Check the current bit of B and the previous bit P_prev.
Here's an example to illustrate Booth's algorithm:
- A = 5 (in binary: 0101)
- B = -3 (in binary using two's complement: 1101)
- Initialize P = 0 and P_prev = 0.
- Process each bit of B from right to left:
- Bit 1: B = 1, P_prev = 0. Add A to P: P = 0101, P_prev = 1.
- Bit 0: B = 0, P_prev = 1. Subtract A from P: P = 0010, P_prev = 0.
- Bit 1: B = 1, P_prev = 0. Add A to P: P = 1010, P_prev = 1.
- Bit 1: B = 1, P_prev = 1. No operation needed.
Q.3 Rules for Performing Arithmetic Operations on Floating Point Numbers
The rules for performing arithmetic operations on floating-point numbers, typically represented in IEEE 754 format, are as follows:
- For addition or subtraction, align the exponents of the operands by shifting the mantissa of the operand with the smaller exponent.
- Add or subtract the mantissas of the aligned operands.
- Normalize the result if necessary by adjusting the exponent and mantissa to ensure proper representation.
- Round the result according to the specified rounding mode.
- For multiplication or division, multiply or divide the mantissas of the operands and add or subtract their exponents.
- Normalize the result if necessary and round it according to the specified rounding mode.
Q.4 Signed Addition and Subtraction with Example
Signed addition and subtraction follow the rules of binary arithmetic, with an additional consideration for sign extension and overflow.
- Example of Signed Addition:
Adding two signed binary numbers:- +5 (in binary: 0101)
- -3 (in binary using two's complement: 1101)
- Example of Signed Subtraction:
Subtracting one signed binary number from another:- +5 (in binary: 0101)
- -3 (in binary using two's complement: 1101)
Q.5 Draw and Explain Four-Bit Carry Look-Ahead Adder
A four-bit carry look-ahead adder (CLA) is a combinational logic circuit used to perform addition of two four-bit binary numbers. It utilizes a carry look-ahead logic to compute the carry-out signals for each bit position simultaneously, improving the speed of addition.
Q.6 Explain Non-Restoring Division with Example
Non-restoring division is a method used to divide two binary numbers without using restoring operations. It involves a series of subtraction and shifting operations to find the quotient and remainder.
Q.7 Design Fast Adder Using n-Bit Ripple Carry Adder
A fast adder can be designed using an n-bit ripple carry adder by incorporating techniques such as carry look-ahead or carry select to reduce the propagation delay associated with ripple carry.
Q.8 Discuss IEEE Standard Floating-Point Formats in Detail
IEEE 754 is a widely used standard for representing floating-point numbers in computer systems. It defines formats for single precision (32 bits) and double precision (64 bits) floating-point numbers, including the sign bit, exponent, and mantissa.
Q.9 Explain Binary Multiplier Using Sequential Circuits
A binary multiplier implemented using sequential circuits utilizes flip-flops and combinational logic to perform multiplication of two binary numbers bit by bit, similar to the manual multiplication method.
Q.10 Explain Binary Multiplication Using Sequential Circuit Multiplier
Binary multiplication using a sequential circuit multiplier involves breaking down the multiplication process into smaller steps, with each step executed sequentially based on the clock signal.
Accessing I/O Devices:
This topic covers the methods and mechanisms used by a computer's CPU to communicate with input/output (I/O) devices, such as keyboards, mice, monitors, disk drives, and network interfaces.
Techniques for accessing I/O devices include programmed I/O, where the CPU directly controls data transfers to and from devices, and memory-mapped I/O, where specific memory addresses are assigned to interact with devices.
Accessing I/O devices efficiently is crucial for the overall performance of a computer system, and various strategies like interrupt-driven I/O and direct memory access (DMA) are employed to optimize data transfer between the CPU and devices.
Interrupts:
Interrupts are signals generated by hardware or software that temporarily suspend the CPU's current execution to handle specific events or conditions.
These events can include I/O requests, timer expirations, or errors detected by hardware components.
When an interrupt occurs, the CPU saves its current state, transfers control to an interrupt handler routine, and upon completion, resumes the interrupted program.
Interrupts are essential for multitasking and real-time processing, allowing the CPU to respond promptly to external stimuli without wasting processing cycles.
Enabling and Disabling Interrupts:
Enabling and disabling interrupts involves controlling the CPU's ability to recognize and respond to interrupt requests.
Enabling interrupts allows the CPU to respond to interrupt signals, whereas disabling interrupts prevents the CPU from acknowledging and servicing interrupts.
This mechanism is used to manage critical sections of code where uninterrupted execution is necessary, such as during the handling of sensitive data or the modification of shared resources.
Handling Multiple Devices:
Modern computer systems often interact with multiple I/O devices simultaneously, requiring efficient management of device interactions.
Techniques for handling multiple devices include interrupt prioritization, where higher-priority interrupts are serviced before lower-priority ones, and interrupt chaining, where multiple interrupt handlers are linked together to handle related events.
Proper management of multiple devices ensures that each device receives timely attention without overburdening the CPU or causing conflicts between devices.
DMA (Direct Memory Access):
DMA is a mechanism that allows peripheral devices to transfer data directly to and from the computer's memory without involving the CPU.
With DMA, a DMA controller coordinates data transfers between devices and memory independently of the CPU, significantly reducing CPU overhead and improving system performance.
DMA is commonly used for high-speed data transfers, such as those required for disk I/O operations or network communications.
I/O Hardware:
I/O hardware refers to the physical components of a computer system that facilitate input and output operations.
This includes devices such as keyboards, mice, displays, printers, disk drives, network interfaces, and expansion cards.
I/O hardware interfaces with the CPU and memory through buses and controllers, enabling data exchange between the computer and its external environment.
Standard I/O Interfaces: SCSI (Small Computer System Interface):
SCSI is a standard interface for connecting peripheral devices such as hard drives, tape drives, optical drives, and scanners to a computer system.
It provides a high-speed, bidirectional communication channel that allows multiple devices to be connected in a daisy-chain or parallel configuration.
SCSI supports advanced features such as command queuing, bus mastering, and hot swapping, making it suitable for demanding storage and data transfer applications in both personal computers and enterprise servers.
