# Binary Numbers

## What is a Numeral?

What is the difference between a number and a numeral?

Number Indo-Arabic Chinese Thai Hebrew Roman
Zero 0
One 1 א I
Two 2 ב II
Three 3 ג III
Four 4 ד IV
Five 5 ה V

Why do we have 10 symbols? Could we use others?

## Our New System

Let’s invent one:

Number Numeral
Zero
One
Two
Three
Four

What if this is all the symbols we had?

## Writing Five

How would we represent five?

No ten symbol: we use a 1 in the tens place.

We use a fives place in our system.

Number Fives Ones Numeral
Five †☉
Six ††
Seven †≈
Eight †△
Nine †✦

The number seven is one × five + two × one.

## Writing Eleven

What about representing ten? Ten is two × five:

Number Fives Ones Numeral
Ten ≈☉
Eleven ≈†
Twelve ≈≈
Thirteen ≈△
Fourteen ≈✦

Thirteen is two × five + three × one.

## Writing Twenty-five

Twenty-four is ✦✦ … four × five + four × one

What is twenty-five?

Like the hundreds place, we a new position for it:

Twenty-fives Fives Ones

Twenty-five is †☉☉, and twenty-six is? Yup: †☉†

What about writing eighty-nine?

## Writing Eighty-Nine

Eighty-nine is 75 + 10 + 4:

Twenty-fives Fives Ones
△ (3) ≈ (2) ✦ (4)

Written: △≈m✦

## Binary Numerals

What if we only had two numerals!? Crazy, huh?

Number Numeral
Zero
One

## Binary Table

Number Eight Four Two Ones Number
Zero
One
Two     ●○
Three     ●●
Four   ●○
Five   ●○●
Six   ●●○
Seven   ●●●
Eight ●○○○
Nine ●○○●
Ten ●○●○

## Why Binary?

Computers only have two digits … an electrical current that is on, and a missing a current that is off.

We call numbers represented with only two symbols, binary.

## Binary Table … Again

Number Eight Four Two Ones Number
Zero       `0` `0`
One       `1` `1`
Two     `1` `0` `10`
Three     `1` `1` `11`
Four   `1` `0` `0` `10`
Five   `1` `0` `1` `101`
Six   `1` `1` `0` `110`
Seven   `1` `1` `1` `111`
Eight `1` `0` `0` `0` `1000`
Nine `1` `0` `0` `1` `1001`
Ten `1` `0` `1` `0` `1010`

## Binary Joke

Telling the computer that the number `1000` is eight instead of one thousand is another story.

Now, you will be able to understand the popular joke:

There are only `10` types of people in the world, Those who understand binary and those that who don’t.

## Hexadecimal

Binary is tedious, decimal notation isn’t good for computers.

Number Sixteen Ones Number
Zero   `0` `0`
One   `1` `1`
Two   `2` `2`
Three   `3` `3`
Four   `4` `4`
Five   `5` `5`
Six   `6` `6`
Seven   `7` `7`
Eight   `8` `8`
Nine   `9` `9`

## Hexadecimal … The Rest

 Ten `A` `A` Eleven `B` `B` Twelve `C` `C` Thirteen `D` `D` Fourteen `E` `E` Fifteen `F` `F` Sixteen `1` `0` `10` Seventeen `1` `1` `11` Eighteen `1` `2` `12` Nineteen `1` `3` `13` Twenty `1` `4` `14` Hundred `6` `4` `64` Two Hundred `C` `8` `C8` Two Hundred and Fifty-five `F` `F` `FF`

Hundred is `64` because six ✕ sixteen is ninety-six plus four is one hundred.

Two hundred is `C8` because `C` is twelve and twelve ✕ sixteen is one-hundred and ninety-two (just add eight more to get two-hundred).

Date: 2014 Nov 01

Created: 2020-12-23 Wed 10:14