9. Principles of Computer Arithmetic in System Design
Computer arithmetic serves as the foundational mathematical framework for digital systems by detailing how numbers are represented and manipulated within hardware. Key elements include different representations of numbers—both signed and unsigned—along with various arithmetic operations such as addition, subtraction, multiplication, and division. Floating-point arithmetic adheres to standards like IEEE 754 to ensure accuracy across computations, while hardware optimization techniques further enhance performance in practical applications.
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What we have learnt
- Computer arithmetic is essential for mathematical processing in digital systems.
- It includes various methods for number representation and performs crucial operations such as addition and multiplication.
- Standards like IEEE 754 guide floating-point operations, while hardware optimization techniques play a significant role in improving efficiency.
Key Concepts
- -- Unsigned Binary Numbers
- A representation of non-negative integers ranging from 0 to 2^n - 1, where n is the number of bits.
- -- Signed Binary Numbers
- A representation that allows for both positive and negative integers, utilizing different formats such as Sign-Magnitude, 1's Complement, and 2's Complement.
- -- FloatingPoint Standard (IEEE 754)
- A technical standard for floating-point computation that defines formats for representing real numbers in binary.
- -- CarryLookahead Adder (CLA)
- An advanced adder that reduces carry propagation delays, resulting in faster arithmetic operations.
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