Clock Arithmetic 7 January 2019 OSU CSE 1 Mathematical Modulo - - PowerPoint PPT Presentation

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Sep 15, 2023 267 likes •366 views

Clock Arithmetic 7 January 2019 OSU CSE 1 Mathematical Modulo (mod) The value of a mod b , or a modulo b , where a and b are mathematical integer s and b > 0 , is computed by doing clock arithmetic on a clock face with b positions

SLIDE 1

Clock Arithmetic

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SLIDE 2

Mathematical Modulo (“mod”)

The value of a mod b, or a modulo b,

where a and b are mathematical integers and b > 0, is computed by doing clock arithmetic on a clock face with b positions

– If a > 0, the “hand” on the clock starts at 0 and moves |a| positions clockwise – If a < 0, it moves |a| counter-clockwise – Where it ends up is the value of a mod b

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SLIDE 3

Example: 24-hr Clock

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SLIDE 4

Example: 24-hr Clock

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Any integer mod 24 is a number between 0 and 23 inclusive.

SLIDE 5

Example: 24-hr Clock

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What is 67 mod 24? Twice around is 48, and 19 more makes

67. Hence, 19.

SLIDE 6

Example: 24-hr Clock

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And (–67) mod 24? Hint: it is not 19, it is not –19, but rather…

SLIDE 7

Example: 24-hr Clock

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And (–67) mod 24? Hint: it is not 19, it is not –19, but rather 5.

SLIDE 8

Modulo ≠ Remainder (%)

What is the remainder upon dividing 67

by 24? It is 19.

What is the remainder upon dividing –67

by 24? It is –19.

– At least most people would say it is, and indeed this is how Java evaluates the expression: (-67) % 24

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