Learning Binary Language
This exercise allows student to explore the logic of the binary language. This will enable
the student to appreciate the complexity of language that can be developed from just 2
digits, the one (1) and the zero (0).
This activity will explain how to make a device so any number can be written by simply
using 1’s and 0’s. Once this is understood, teachers and students can take the idea of
binary language into any number of directions.
Materials:
paper and pencil
masking tape
standard ice cube tray
pennies (16 per ice cube tray)
Set up
1. Using the masking tape place a piece across each row along the long side of the ice
cube tray.
2. Starting in the right hand lower corner of the tray label the opening 20.
Any number to the power of 0 is equal to 1.
(i.e.: 20=1, 1230=1)
3. Label the next opening to the left 21.
Any number to the power of 1 is equal to the base number.
(i.e.: 21=2, 1231=123)
4. Label the next opening to the left 22.
The power of a number represents the number of times the base number will be
multiplied times itself.
(i.e.: 22=2x2=4, 23=2x2x2=8)
5. Label the remaining openings so your try looks like the figure below.
This should be enough information for most activities however, students are welcome to
calculate the numbers for the remaining openings.
28 (128)
26 (64)
25 (32)
24 (16)
23 (8)
210
(1024)
29 (512)
28 (256)
22 (4)
21 (2)
20 (1)
6. Instructions for making binary numbers.
a. put a penny into the openings necessary for creating the sum equal to the needed
number.
For example this is where pennies are placed to make the number 10. There is a penny in
the (2) opening and the (8) opening, 2 + 8 = 10.
28 (128)
26 (64)
25 (32)
24 (16)
23 (8)
210
(1024)
29 (512)
28 (256)
22 (4)
21 (2)
20 (1)
P
P
b. To write the binary number for the quantity of 10 start with the penny that is farthest
away from the 20 (1) opening and write a 1 for each penny and a 0 for each empty
opening. Using this method the binary number for 10 is 1010.
Further examples:
The quantity 13 is 1101
28 (128)
26 (64)
25 (32)
24 (16)
210
(1024)
29 (512)
28 (256)
23 (8)
22 (4)
21 (2)
20 (1)
P
P
P
The quantity 863 is 1101011111
(This one will keep your students busy for a few minutes)
28 (128)
26 (64)
25 (32)
P
210
(1024)
29 (512)
28 (256)
P
P
24 (16)
23 (8)
22 (4)
21 (2)
20 (1)
P
P
P
P
P
This is how to explain the binary system by making an ice cube tray translator. Where
you and your students take the idea of binary language is up to you.
Dr. Robert Price, price@nvnet.org