Applied maths- coding
LO To learn basic computer coding using binary
•
•
•
Pick a number 1 to 31 and tell
me in which columns your
number is present in the grid.
Be careful to check all
columns.
Example – No. 23 is in
columns 1, 3, 4 & 5.
Col
1
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Col
2
8
9
10
11
12
13
14
15
24
25
26
27
28
29
30
31
Col
3
4
5
6
7
12
13
14
15
20
21
22
23
28
29
30
31
Col
4
2
3
6
7
10
11
14
15
18
19
22
23
26
27
30
31
Col
5
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
How does this work?
Only 4 columns here
Can you spot the trick now?
Pick a number 1 to 15 and tell
me in which columns your
number is present in the grid.
Tell me the number at the
top of each column where
your number is present.
8 Col
9 1
8
10
9
11 10
12 11
13 12
14 13
14
15
15
4Col
52
4
6
5
76
127
1312
1413
14
15
15
2
Col
33
2
6
3
76
107
10
11
11
14
14
15
15
Any ideas?
1
Col
43
1
5
3
57
79
9
11
11
13
13
15
15
Explanation
So this is how the game is
played:Pick a number -
6
At the top of the columns
where 6 is present we have
4 & 2.
4+2=6
8
4
2
1
9
5
3
3
10
6
6
5
11
7
7
7
12
12
10
9
13
13
11
11
14
14
14
13
15
15
15
15
Your turn
Looking at the top two rows we
see:
Col Col Col Col Col
1
16
2
8
3
4
4
2
5
1
Pick a number - 𝒙
𝒙 is in columns 1, 3, 4 & 5.
A bit of practice needed to
remember the top row numbers
16 + 4 + 2 + 1 = 23
Now you can impress your
friends with this trick!
Col
1
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Col
2
8
9
10
11
12
13
14
15
24
25
26
27
28
29
30
31
Col
3
4
5
6
7
12
13
14
15
20
21
22
23
28
29
30
31
Col
4
2
3
6
7
10
11
14
15
18
19
22
23
26
27
30
31
Col
5
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
Binary Code
01000010011010010110111001100001011100
10011110010010000001000011011011110110
010001100101
Computers are not as smart as you think, in
fact, they only know 2 things…
0 and 1
Everything else is told to the computer by a
human, this is called programming.
For a computer
0 means turn a circuit off
1 means turn a circuit on
Humans need to learn the
computer’s language to be able
to tell computers what to do.
Computer language is Binary.
Here is an example of what binary code looks like:
010101000110100001101001011100110010000001
101001011100110010000001100101011000010111
0011011110010000110100001010
The computer
can only use 0s
and 1s
So for a computer
numbers go like is
this…
Denary (our numbers)
Binary
0
1
2
3
4
5
6
7
8
9
10
11
12
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
Method
Make a table like this..
128 64 32 16
8
4
2
1
To make the number 5, place a 1 under the numbers
that you need and a 0 under the numbers that you
don’t…
128 64
0
0
32
16
8
4
2
1
0
0
0
1
0
1
This is
Binary
So 5 for us, is 00000101 for the computer
128 64
0
0
32
16
8
4
2
1
0
0
0
1
0
1
101
ACTIVITY
Convert binary to denary digits
a)
128 64
32
16
8
4
2
1
1
0
0
0
0
1
0
128 64
32
16
8
4
2
1
0
1
0
0
1
0
1
128 64
32
16
8
4
2
1
0
0
0
0
0
1
0
b)
0
c)
1
0
ACTIVITY
Convert binary to denary digits
a)
128 64
0
1
32
16
8
4
2
1
0
0
0
0
1
0
64 + 2 = 66
ACTIVITY
Convert binary to denary digits
b)
128 64
0
0
32
16
8
4
2
1
1
0
0
1
0
1
32 + 4 + 1 = 37
ACTIVITY
Convert binary to denary digits
c)
128 64
1
0
32
16
8
4
2
1
0
0
0
0
0
1
128 + 1 = 129
ACTIVITY
1. Show your shoe size in binary
2. Show the date of the month you were born in
binary
3. Show your age in binary
4. Show your height in cm in binary
5. Show the amount of siblings you have in binary
6. Show your house number in binary
ACTIVITY
Working in pairs;
• give your partner any number under 255
• see if they can convert it into binary.
>>>EXT
Is there any number that CAN’T be made?
ACTIVITY
Use your table to convert
these numbers to binary:
3
2
0
6
10
17
20
>>>EXT: 42
47
71
146
255
Answers
>>>EXT:
3
2
0
6
10
17
20
42
47
71
146
255
11
10
0
110
1010
10001
10100
101010
101111
1000111
10010010
11111111
ACTIVITY
Convert these binary numbers into denary
a) 00011000
b) 00000101
c) 00010110
d) 01101011
e) 01111000
f) 10100100
g) 10100101
h) 10111100
i) 11010111
j) 11100110
k) 11111010
Answers
24
5
22
107
120
164
165
188
215
230
250
00011000
00000101
00010110
01101011
01111000
10100100
10100101
10111100
11010111
11100110
11111010
ACTIVITY
De-code the following:
11001% of people in the world do not have access to a
mobile phone.
Gorillas sleep as much as 1110 hours per day.
You can tell the sex of a horse by its teeth. Most males
have 101000, females have 100100.
On average, 1100 newborns will be given to the wrong
parents daily.
A giraffe can clean its ears with its 10101 inch tongue!
A man named Charles Osborne had the hiccups for
1000101 years!
Answers
De-code the following:
25% of people in the world do not have access to a
mobile phone .
Gorillas sleep as much as fourteen hours per day.
You can tell the sex of a horse by its teeth. Most males
have 40, females have 36.
On average, 12 newborns will be given to the wrong
parents daily.
A giraffe can clean its ears with its 21 inch tongue!
A man named Charles Osborne had the hiccups for 69
years!
GAME
Binary code is not just about numbers. Every
number, letter and symbol on your keyboard
needs to be converted into binary so the
computer can understand it.
We can see all these conversions in
something called an ASCII table.
Symbol
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Decimal
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
Binary
01000001
01000010
01000011
01000100
01000101
01000110
01000111
01001000
01001001
01001010
01001011
01001100
01001101
01001110
01001111
01010000
01010001
01010010
01010011
01010100
01010101
01010110
01010111
01011000
01011001
From
the
ASCII
table…
Symbol
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
Decimal
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
Binary
01100001
01100010
01100011
01100100
01100101
01100110
01100111
01101000
01101001
01101010
01101011
01101100
01101101
01101110
01101111
01110000
01110001
01110010
01110011
01110100
01110101
01110110
01110111
01111000
01111001
You can write your name in binary…
H a n n
a h
010010000110000101101110011011100110000101001000
Every time you type a letter on your
keyboard, the computer understands is
as loads of 0s and 1s!
Here are some other characters you
might need from the ASCII table…
Symbol
Space
!
"
#
$
%
&
'
(
)
*
+
,
.
/
:
;
<
=
>
?
Decimal
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
58
59
60
61
62
63
Binary
00100000
00100001
00100010
00100011
00100100
00100101
00100110
00100111
00101000
00101001
00101010
00101011
00101100
00101101
00101110
00101111
00111010
00111011
00111100
00111101
00111110
00111111
Symbol
@
[
\
Decimal
64
91
92
Binary
01000000
01011011
01011100
]
^
_
`
{
¦
}
93
94
95
96
123
124
125
01011101
01011110
01011111
01100000
01111011
01111100
01111101
~
126
01111110
Decode this message:
010010010110011000100000011110010110
111101110101001000000110001101100001
011011100010000001110010011001010110
000101100100001000000111010001101000
011010010111001100100000011110010110
111101110101001000000110100001100001
011101100110010100100000011000110111
001001100001011000110110101101100101
011001000010000001100010011010010110
111001100001011100100111100100100001