[CA] Lecture #11

Chapter 3: Arithmetic for Computers

 

Extra (From Digital Logic Class)

Unsigned Integers

Decimal & Binary Number

 

Octal & Hexadecimal Number

 

Binary to Octal and Hexadecimal

 

 

Signed Number

 

1) Sign-and-Magnitude Representation

 

2) 1's Complement Representation

: 뒤집기만!

 

3) 2's Complement Representation

: 뒤집고, +1!

 

 

Four-bit Signed Integers

 

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Addition

1) Sign and Magnitude

 

2) 1's Complement

 

3) 2's Complement

 

 

Subtraction: 2's Complement

: Addition과 같은 방법으로 계산한다.

 

 

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Integer Addition

 

Integer Subtraction

 

Overflow

• (+) + (+) = (-)
• (-) + (-) = (+)

 

Arithmetic Logic Unit (ALU) Design

• ALU: A divice that performs the arithmetic operations like addition and subtraction or logical operations like AND or OR.

 

Full Adder (1-Bit)

 

Ripple Carry Adder

 

A Hierarchical Carry-Lookahead Adder

 

Adder and Subtractor Unit

 

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Arithmetic for Multimedia

• SIMD (Single-Instruction, Multiple-Data)
• Saturating operations --> Overflow 발생하면, 표현 가능한 가장 큰 양수로 표현한다.