| Creator | Mikko Muilu |
| Subject | Math, ICT |
| Length | 45 minutes |
| Pedagogical Approach | Phenomenon-based learning |
| Competences | Students learn to do basic math using cards and binary numbers |
| Grades | Students aged 9-12. |
| Technologies | Pen and paper |
Description:
Computers are made of transistors and they can’t calculate or understand numbers in the very basic level like we do. Computers work with ones and zeros, which can be marked with electrical voltage on or off. No voltage means 0 and voltage on means 1. This is easy enough to understand, but what if we need other numbers or other symbols than just 0’s and 1’s.
Students are already familiar with binary numbers, but now we try to do basic math with them. Let’s remind ourselves how we add with normal numbers from 0-9.
7 + 5
Calculating this with long addition is familiar. Notice the carry in red.
Long adding works similarly in binary numbers. Here’s a quick reminder about the 3-bit binary numbers.
000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7
The basic adding is quite easy to grasp.
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10, which is 1+1 = 2 but in binary.
Long addition works like this in binary
Above calculation is 2 + 3 in binary. Notice how 0 + 1 is 1 in rightmost column. 1 + 1 is 0 and carries 1.
Above calculation is 3 + 3 in binary. Notice how 1 +1 is 0 in rightmost column as 1 is carried to the next column. In the middle 1 + 1 + carry 1 is 1 and carries 1.
Exercise 1:
Teachers gives out 3-bit binary numbers for pairs of students and students try to add them together. Students can use binary cards to decode the value of binary numbers.
Disclaimer: This will take time and is hard to grasp at first. Students are familiar with numbers 0-9 and it is really hard to do even easy calculations in binary numbers 0-1.
Discussion:
What was hard? How did the calculation go? How hard would the calculations be if more bits were added?
Exercise 2:
Calculations with 5-bit binary numbers. Students can use binary cards to decode the value of binary numbers. They can check answers via changing the binary numbers to decimal numbers
For example
01001 + 00010
00100 + 00100
01111 + 00001
Discussion:
Computers have basic mathematical operations like addition and subtraction programmed into them. Adding in binary is simple and it is fairly easy to do with basic logic ports in electronics.