[컴퓨터구조] 3. Arithmetic for Computers (4)

Division Overview

Division Overview

• Dividend: 나눠지는 수
• Divisor: 나누는 수
• Quotient: 몫
• Remainder: 나머지

 

Division Hardware

Division Hardware - 1st version

Division Hardware - 1st version

 

Division Hardware - 2nd version

Division Hardware - 2nd version

 

Division Hardware - 3rd version

Division Hardware - 3rd version

 

Dividing Signed Numbers

1. Dividend(나눠지는 수), Divisor(나누는 수)의 sign bit 확인하기
2. Quotient(몫): 두 수의 sign bit이 서로 다르면, 음수이다.
3. Remainder(나머지): Dividend(나눠지는 수)와 부호가 같다.

 

MIPS Divide Instructions

▶ Results in Lo, Hi registers:

• Lo: Quotient(몫)
• Hi: Remainder(나머지)

▶ Divide Instructions:

div  $s0, $s3
divu $s0, $s3

▶ Divide pseudo instructions:

div  $s3, $s2, $s1    # $s3 = $s2/$s1
divu $s3, $s2, $s1

• Software must check for overflow, divide-by-zero.

 

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Fixed Point Representation

Fixed Point Representation

 

Another Approach: Scientific Notation (10진수)

: Mantissa (significand; normalized number) + Exponent (base 10)로 수를 표현하는 방법

예) 6.02 * 10^23

• Mantissa (significand) = 6.02
• Radix (base) = 10 (10진수)
• Exponent = 23

 

Floating Point (2진수)

Floating Point (2진수)

1) Single-Precision

예) 8.75

--> 8 = 1000

--> 0.75 = 0.11

--> 8.75 = 1000.11

--> Normalization = 1.00011 (* 2^3 필요)

• S = 0 (양수)
• Exponent = 3 + Bias(127) = 130
• Significant = 00011...

1) Single-Precision

 

2) Double-Precision

• S = 0 (양수)
• Exponent = 3 + Bias(1023) = 1026
• Significant = 00011...