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Pick a number between 1 and 63 (inclusive)
tell me which boxes the number appears in
I will tell you what your number is

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10110

What is this number ?

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10⁴

10³

10²

10¹

10⁰

10000

1000

100

10

1

decimal (base 10)

0

1

0

1

1 x 10000 = 10000

0 x 1000 = 0

1 x 100 = 100

1 x 10 = 10

0 x 1 = 0

10110

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10⁴

10³

10²

10¹

10⁰

10000

1000

100

10

1

decimal (base 10)

2

0

7

9

5

5 x 10000 = 50000

2 x 1000 = 2000

0 x 100 = 0

7 x 10 = 70

9 x 1 = 9

52079

6 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

binary (base 2)

16

8

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

hexadecimal (base 16)

2⁸

2⁷

2⁶

2⁵

64

32

256

128

10⁴

10³

10²

10¹

10⁰

10000

1000

100

10

1

decimal (base 10)

2

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2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

0

1

0

1

1 x 16 = 16

0 x 8 = 0

1 x 4 = 4

1 x 2 = 2

0 x 1 = 0

22

binary (base 2)

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2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

1

0

1

0

1

0

1

1 x 128 = 128

1 x 32 = 32

1 x 16 = 16

1 x 8 = 8

1 x 2 = 2

186

0

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2⁴

2³

2²

2¹

2⁰

2⁸

2⁷

2⁶

2⁵

4

2

1

16

8

64

32

256

128

1

0

1

0

1

0

1 x 64 +

1 x 8 +

1 x 2 +

1 x 1 = 75

10 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

Which place value must you have for all odd numbers

What is the first number that must have the place value

4

2

What is the first number that must have the place value

What is the LARGEST number you can make with the first 6 place values

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Person 1 picks a number between 1 and 63 (inclusive)
Person 1 says which boxes the number appears in
Person 2 determines the number

HINT #4

The numbers in a box are ALL the numbers btw 1 and 63 that have �a 1 in the place value given by the number in the top LEFT of the box..

HINT #3

What box has all the numbers greater than 32?

HINT #2

What number is in the top left corner of the box that has all the odd numbers?

HINT #1

Which box has all the odd numbers btw 1 and 63?

12 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

28₁₀ = ? ₂

13 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

1

0

1

0

28₁₀ = 11100 ₂

28 - 16 = 12

12 - 8 = 4

4 - 4 = 0

28₁₀ = ? ₂

If remaining number is greater or equal to the largest remaining place value put a 1 for that place value & subtract number from that place value. Repeat.

14 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

238₁₀ = ? ₂

tinyurl.com/LASACSpoll

15 of 37

2⁴

2³

2²

2¹

2⁰

4

2

1

16

8

2⁸

2⁷

2⁶

2⁵

64

32

256

128

238₁₀ = 11101110 ₂

1

0

1

0

238 - 128 = 110

110 - 64 = 46

2 - 2 = 0

46 - 32 = 14

14 - 8 = 6

6 - 4 = 2

238₁₀ = ? ₂

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All data in a computer is stored as a binary number.

Depending on context, the binary value 11100101 can be interpreted by the computer as

the positive integer 229
the negative integer -27
the character σ (sigma)

the red level of a pixel (229 out of 255)

an instruction to the processor (e.g. add 2 numbers)
⋮ ⋮ ⋮

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Why do computers use binary to store data?

Because a binary digit can only represent one of TWO values

0 or 1 ( a decimal digit represents TEN values 0 一 9 )

It is much easier to build fast circuits that only have to distinguish between TWO values

1 = there is a charge/voltage/light
0 = there is no charge/voltage/no light

Transistors used in computers are small switches that can be switched between ON and OFF very fast and can be used to build tiny logic gates that implement binary logic.

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Perseverance

rover

Mars Landing

Feb 18, 2021

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2⁴

2³

2²

2¹

2⁰

4

2

1

binary (base 2)

16

8

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

hexadecimal (base 16)

2⁸

2⁷

2⁶

2⁵

64

32

256

128

10⁴

10³

10²

10¹

10⁰

10000

1000

100

10

1

decimal (base 10)

2

24 of 37

0 1 2 3 4 5 6 7 8 9

Decimal is base 10 with 10 "symbols"

0 1

Binary is base 2 with 2 "symbols"

0 1 2 3 4 5 6 7 8 9 ? ? ? ? ? ?

Hexadecimal is base 16 with 16 "symbols"

0 1 2 3 4 5 6 7 8 9 A B C D E F

10 11 12 13 14 15

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16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

2

4

A

C

2 x 4096 = 8192

4 x 256 = 1024

10 x 16 = 160

12 x 1 = 12

9388

0

26 of 37

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

0

A

C

E

0

ACE₁₆ = ? ₁₀

tinyurl.com/LASACSpoll

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16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

0

A

C

E

10 x 256 = 2560

12 x 16 = 192

14 x 1 = 14

2766

0

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16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

9279₁₀ = ? ₁₆

29 of 37

9279₁₀ = 243F₁₆

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

2

4

3

F

9279 - 2(4096) = 1087

15 - 15(1) = 0

1087 - 4(256) = 63

63 - 3(16) = 15

9279₁₀ = ? ₁₆

0

30 of 37

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

636₁₀ = ? ₁₆

tinyurl.com/LASACSpoll

31 of 37

636₁₀ = 27C₁₆

16⁴

16³

16²

16¹

16⁰

65536

4096

256

16

1

0

2

7

C

12 - 12(1) = 0

636 - 2(256) = 124

124 - 7(16) = 12

636₁₀ = ? ₁₆

0

32 of 37

What is the value of LASA₃₂?

(21 x 32³) + (10 x 32²) + (28 x 32) + 10 = 699274

Base 32?

33 of 37

xkcd.com/2835

explained

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Using a base other than 2, 10, or 16

What base would you have to use to make you "appear" to be 18 years old ?

13_?? = 18₁₀

13₁₅ = 1 x 15¹+ 3 x 15⁰ = 18₁₀

14_?? = 18₁₀

14₁₄ = 1 x 14¹+ 4 x 14⁰ = 18₁₀

15_?? = 18₁₀

15₁₃ = 1 x 13¹+ 5 x 13⁰ = 18₁₀

16_?? = 18₁₀

16₁₂ = 1 x 12¹+ 6 x 12⁰ = 18₁₀

17_?? = 18₁₀

17₁₁ = 1 x 11¹+ 7 x 11⁰ = 18₁₀

What base would you have to use to claim to be 29 years old when you were in fact 39 ?

29_?? = 39₁₀

29₁₅ = 39₁₀

13₁₆ = 18₁₀

13₁₆ = 1 x 16¹+ 3 x 16⁰ = 19₁₀

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binary is the same as base 2

decimal is the same as base 10

hexadecimal is the same as base 16

36 of 37

binary numbers

Converting from decimal to binary

Converting from decimal to hexadecimal representation

Converting larger number from decimal to binary

Converting directly from binary to hexadecimal

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Hex Shortcut Tables Presentation

What's next ...

1st

2nd

3rd

4th

LASACS

Hex Shortcut How & Why

Number Conversion Worksheet