Computer Arithmetic

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Computer Arithmetic by Mind Map: Computer Arithmetic

1. Aspects

1.1. Hardware

1.2. Software

2. Software

2.1. Complexity

2.2. Error Characteristics

2.2.1. Computational Error

2.2.2. Representation Error

2.2.3. Catastrophic Cancellation

2.3. Stability

2.4. Computer Algorithm Certifiability

2.4.1. Interval Arithmetic

3. Hardware

3.1. Adders

3.1.1. Half-adder

3.1.2. Bit Serial adder

3.1.3. Ripple Carry adder

3.1.4. Full adder

3.2. Subtractors

3.2.1. As in Adders

3.3. Multipliers

3.3.1. Partial Product bit-matrix

3.3.2. High-radix Multipliers

3.3.3. Fast Multipliers

3.4. Dividers

3.4.1. Quotient Digit

3.4.2. Partial Remainder

3.4.3. High-radix Dividers

3.4.4. Array Dividers

3.5. Square-rooters

3.6. Function Evaluators

3.6.1. Synchronous Counters

3.6.2. Up-counters

3.6.3. Down-counters

4. Numbers

4.1. Digit Sets and Encoding

4.1.1. BCD

4.1.2. ASCII

4.1.3. Biased Representation (Signed nos)

4.2. Types

4.2.1. signed

4.2.1.1. Integers

4.2.1.2. Reals

4.2.2. Unsigned

4.2.2.1. Whole Numbers

4.3. Representation

4.3.1. Unary code

4.3.2. radix-10

4.3.3. radix-2

4.3.4. Roman numerals

4.3.5. Other radices

4.3.5.1. radix-60

4.3.5.2. radix-16

4.3.5.3. radix-8

4.4. Floating-point numbers

4.4.1. IEEE 754 Standard

4.4.1.1. sign

4.4.1.2. exponent

4.4.1.3. Mantissa

4.4.2. 32-bit

4.4.3. 64-bit

4.5. Fixed-point numbers