From decimal to binary
Choose a number and run the algorithm that turns it into binary: divide by 2, keep the remainder as the next bit, and repeat until nothing is left. Watch the bits build up from the right and count how many a number needs.
Core concept
Repeatedly dividing a number by 2 gives its binary digits as the remainders, from the last bit to the first; each remainder is placed one place further left
Topic: Programming basics
We count in decimal, with ten digits, 0 to 9. Computers store everything with only two, 0 and 1, called bits: binary: Counting with only two digits, 0 and 1. Computers store everything this way. All key words. To turn a decimal number into binary there is a simple algorithm: A list of clear steps that solves a problem, like a recipe. All key words. Divide the number by 2: the remainder, 0 or 1, is the last bit. Then divide what is left by 2 again: that remainder is the bit before it. Keep going until nothing is left. The program builds the answer as it goes: each new bit goes one place further left, so it is multiplied by place, which starts at 1 and grows 1, 10, 100, 1000… For 13 the remainders are 1, 0, 1, 1, so 13 in binary is 1101: 8 + 4 + 0 + 1.
What you will learn
- Turn a decimal number into binary by dividing by 2.
- Explain why the first remainder is the last bit.
- Trace a while loop with % 2 and floor(n / 2).
- Check a binary number by adding up its place values.
Before you start
- Know place value in decimal, and remainders.
Materials
- A notebook to write the remainders
Equipment
- None
Procedure
- Step through the program for 13.
- Run it for 5, 6 and 25.
- Run it for 100 and count the bits.
- Answer the practice challenges.