recurse center <3
⚠ technical digression ⚠
"Decimal"
"Base 10"
"Decimal"
"Base 10"
first weird thing: from now on, we will start counting at zero
"decimal"
"base 10"
something interesting happens here!
"base 9"
"base 9"
"octal"
"base 8"
POWER
OF TWO!
"base 3"
drumroll...
"binary!!!!!!!!"
"base 2"
POWER
OF TWO!
Decimal | Binary |
---|---|
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
... |
Decimal | Binary |
---|---|
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
11 | 1011 |
12 | 1100 |
13 | 1101 |
14 | 1110 |
15 | 1111 |
16 | 10000 |
0000 |
0001 |
0010 |
0011 |
0100 |
0101 |
0110 |
0111 |
1000 |
1001 |
1010 |
1011 |
1100 |
1101 |
1110 |
1111 |
eg: 9201
place | name |
---|---|
1 | "ones" |
10 | "tens" |
100 | "hundreds" |
1000 | "thousands" |
⚠ technical digression ⚠
eg: 9201
place | name |
---|---|
1 | "ones" |
10 | "tens" |
100 | "hundreds" |
1000 | "thousands" |
= 9000 + 200 + 0 + 1
= 9201
⚠ technical digression ⚠
eg: 9201
place | name | aka |
---|---|---|
1 | "ones" | 100 |
10 | "tens" | 101 |
100 | "hundreds" | 102 |
1000 | "thousands" | 103 |
= 9000 + 200 + 0 + 1
= 9201
⚠ technical digression ⚠
place | name | i.e. |
---|---|---|
1 | "ones" | 2 0 |
10 | "twos" | 2 1 |
100 | "fours" | 2 2 |
1000 | "eights" | 2 3 |
0 | 0 |
1
|
1
|
10
|
2 |
11 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
1000 | 8 |
1001 | 9 |
1010 | 10 |
⚠ technical digression ⚠
eg: 1001
place | name | i.e. |
---|---|---|
1 | "ones" | 2 0 |
10 | "twos" | 2 1 |
100 | "fours" | 2 2 |
1000 | "eights" | 2 3 |
= 8 + 0 + 0 + 1
= 9
⚠ technical digression ⚠
eg: 0111
place | name | i.e. |
---|---|---|
1 | "ones" | 2 0 |
10 | "twos" | 2 1 |
100 | "fours" | 2 2 |
1000 | "eights" | 2 3 |
= 0 + 4 + 2 + 1
= 7
⚠ technical digression ⚠
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …
⚠ technical digression ⚠
add some new digits here!
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, …
⚠ technical digression ⚠
12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, …
… 99, 9A, 9B, 9C, 9D, 9E, 9F, F0, F1, F2, …
… F9, FA, FB, FC, FD, FE, FF, 100, 101, 102, …
POWER
OF TWO!
(foreshadowing snacks!)
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P |
00000010000001100000011100001111
0
1
2
4
1
2
3
8
8
256
9
512
10
1024
17
131,072
18
262,144
25
33,554,432
= 33,949,455 :/
Every number is made of
exactly 8 bits (1s and 0s)
The highest number is only 255!
11111111 = 1 + 2 + ... + 127 = 255
00000010000001100000011100001111
00000010 00000110 00000111 00001111
= 2
= 6
= 7
= 15
= C
G
H
P ?????
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P |
0=[NUL] 1=[SOH] 2=[STX] 3=[ETX] 4=[EOT] 5=[ENQ] 6=[ACK] 7=[BEL] 8=[BS] 9=[HT] 10=[LF] 11=[VT] 12=[FF] 13=[CR] 14=[SO] 15=[SI] |
16=[DLE] 17=[DC1] 18=[DC2] 19=[DC3] 20=[DC4] 21=[NAK] 22=[SYN] 23=[ETB] 24=[CAN] 25=[EM] 26=[SUB] 27=[ESC] 28=[FS] 29=[GS] 30=[RS] 31=[US] |
32=" " 33=! 34=" 35=# 36=$ 37=% 38=& 39=' 40=( 41=) 42=* 43=+ 44=, 45=- 46=. 47=/ |
48=0 49=1 50=2 51=3 52=4 53=5 54=6 55=7 56=8 57=9 58=: 59=; 60=< 61== 62=> 63=? |
64=@ 65=A 66=B 67=C 68=D 69=E 70=F 71=G 72=H 73=I 74=J 75=K 76=L 77=M 78=N 79=O |
80=P 81=Q 82=R 83=S 84=T 85=U 86=V 87=W 88=X 89=Y 90=Z 91=[ 92=\ 93=] 94=^ 95=_ |
96=` 97=a 98=b 99=c 100=d 101=e 102=f 103=g 104=h 105=i 106=j 107=k 108=l 109=m 110=n 111=o |
112=p 113=q 114=r 115=s 116=t 117=u 118=v 119=w 120=x 121=y 122=z 123={ 124=| 125=} 126=~ 127=[DEL] |
---|
dec | hex | binary | ascii |
---|---|---|---|
65 | 0x41 | 0b01000001 | A |
66 | 0x42 | 0b01000010 | B |
67 | 0x43 | 0b01000011 | C |
68 | 0x44 | 0b01000100 | D |
69 | 0x45 | 0b01000101 | E |
70 | 0x46 | 0b01000110 | F |
71 | 0x47 | 0b01000111 | G |
72 | 0x48 | 0b01001000 | H |
73 | 0x49 | 0b01001001 | I |
74 | 0x4A | 0b01001010 | J |
75 | 0x4B | 0b01001011 | K |
76 | 0x4C | 0b01001100 | L |
77 | 0x4D | 0b01001101 | M |
78 | 0x4E | 0b01001110 | N |
79 | 0x4F | 0b01001111 | O |
dec | hex | binary | ascii |
---|---|---|---|
80 | 0x50 | 0b01010000 | P |
81 | 0x51 | 0b01010001 | Q |
82 | 0x52 | 0b01010010 | R |
83 | 0x53 | 0b01010011 | S |
84 | 0x54 | 0b01010100 | T |
85 | 0x55 | 0b01010101 | U |
86 | 0x56 | 0b01010110 | V |
87 | 0x57 | 0b01010111 | W |
88 | 0x58 | 0b01011000 | X |
89 | 0x59 | 0b01011001 | Y |
90 | 0x59 | 0b01011010 | Z |
H
E
L
L
O
01001000 01000101 01001100 01001100 01001111
dec | hex | binary | ascii |
---|---|---|---|
65 | 0x41 | 0b01000001 | A |
66 | 0x42 | 0b01000010 | B |
67 | 0x43 | 0b01000011 | C |
68 | 0x44 | 0b01000100 | D |
69 | 0x45 | 0b01000101 | E |
70 | 0x46 | 0b01000110 | F |
71 | 0x47 | 0b01000111 | G |
72 | 0x48 | 0b01001000 | H |
73 | 0x49 | 0b01001001 | I |
74 | 0x4A | 0b01001010 | J |
75 | 0x4B | 0b01001011 | K |
76 | 0x4C | 0b01001100 | L |
77 | 0x4D | 0b01001101 | M |
78 | 0x4E | 0b01001110 | N |
79 | 0x4F | 0b01001111 | O |
dec | hex | binary | ascii |
---|---|---|---|
80 | 0x50 | 0b01010000 | P |
81 | 0x51 | 0b01010001 | Q |
82 | 0x52 | 0b01010010 | R |
83 | 0x53 | 0b01010011 | S |
84 | 0x54 | 0b01010100 | T |
85 | 0x55 | 0b01010101 | U |
86 | 0x56 | 0b01010110 | V |
87 | 0x57 | 0b01010111 | W |
88 | 0x58 | 0b01011000 | X |
89 | 0x59 | 0b01011001 | Y |
90 | 0x59 | 0b01011010 | Z |
???
00000010 00000110 0000111 00001111
[stx]
00000010 00000110 00000111 00001111
[ack]
[bel]
[si]
????
0=[NUL] | 1=[SOH] | 2=[STX] | 3=[ETX] | 4=[EOT] | 5=[ENQ] | 6=[ACK] | 7=[BEL] |
---|---|---|---|---|---|---|---|
8=[BS] | 9=[HT] | 10=[LF] | 11=[VT] | 12=[FF] | 13=[CR] | 14=[SO] | 15=[SI] |
⚠ technical digression ⚠
text: it�s hard
⚠ technical digression ⚠
(Object #1)
Ailadi, 2018
Raphael Lozano-Hemmer (2011)
Nitcha Fame Tothong (2018)