# 2024-03-06

## Introduction

> **Summary**

> **keywords**

> **TODO**

> **HW**

> **Exercise**\*

> **Next time**

***

## Information Representations (Cont'd)

### What is a Base-r system?

> Nam's note, Lec. 2 page 15

![image](https://3863748873-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F7lhTZlN8P2dz9Om0Ykpg%2Fuploads%2Fgit-blob-ca9af9169c5544332d8931842e8f5350b5c720b1%2F20240306132229.png?alt=media)

\*\*concept is the number. \*\*\
\*\* Its representation written down works on base-r system. \*\*

#### How do we convert into new base system?

> divide by base, and remainder repeatedly is written from the right.

**How do we do conversion easily on our brain?**

subtract the biggest subtractable geometric progression of the base.

### Fraction conversion

> multiply by base, and take the integer.

> The only purpose of using octal numbers or hexadecimal is for compression

## complements

#### Diminished radix complement

* (r-1)'s complement of N :\
  $(r^n-1)-N$
* r's complement of N:\
  $(r^n) -N$
