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Counting: Decimal to binary
1. Counting: Decimal to binary
2. Algorithms
An algorithm is a precise step by step method to (eventually) solve a (well-defined) problem.
A major part of computer science is the study of data structures and algorithms.
Aside: A less-precise way of solving a problem based on ideas is called a heuristic.
We will look at an algorithm to convert a decimal number x to binary.
3. Manually
Manual method to convert a decimal number
x to binary:
Step 1. If
x is
0, then the binary number is
0. Otherwise, do step 2.
Step 2:While
x is not
0, divide
x by
2 to get a quotient
q and a remainder
r in the range
0 to
1. Write the remainder
r to the left of any previously written binary digits. Replace
x with
q. Repeat step 2.
4. Example: manual method
Example: Convert
156d to binary.
156 divided by 2 is 78 with remainder of 0.
78 divided by 2 is 39 with remainder of 0.
39 divided by 2 is 19 with remainder of 1.
19 divided by 2 is 9 with remainder of 1.
9 divided by 2 is 4 with remainder of 1.
4 divided by 2 is 2 with remainder of 0.
2 divided by 2 is 1 with remainder of 0.
1 divided by 2 is 0 with remainder of 1.
So,
156d is
10011100b =
27 + 24 + 23 + 22 =
128+16+8+4.
Remember the powers of two from the NCAA basketball tournament problem, 1, 2, 4, 8, 16, 32, and 64.
5. Decimal to binary
The best way to learn base conversion is to practice converting some numbers.
A way to check your conversion work is to use the base converter at
Online base converter
6. End of page
