Mathematics Math Shortcuts How to Convert a Number to Binary
How to Convert a Number to Binary
Written by Andrew B. Bartels, October 2011
Here is an easy method to convert any decimal number to binary. If you're without a scientific calculator, this technique is easy enough to be worked out on the back of a napkin.
Steps:
1. Start by writing a column of numbers. On the first row, write down the decimal number you wish to convert.
2. In the next row, write the value above it divided by 2. Write only the integer portion of the number, ignoring any fractional part. Repeat this step until the value written is 1.
3. Start a second column of numbers, to the right of the first. In this column, write a 1 if the number beside it is odd, or a zero if the number beside it is even. Write down a column of 1's and 0's corresponding to each number in the first column.
4. Starting from the bottom of the second column and working upward, write down the 1's and 0's, from left to right. The bottom digit (1 or 0) is written first. Then the second from bottom is written, and so on for each binary digit. The resulting digits are the binary representation of the number you started with.
Example 1: Convert the number 46 to binary
1. Start by writing down the number as a start of a new column.
| 46 |
2. Fill out the rest of the column by dividing the number above it by 2. Write only the integer portion of each value, and use this integer value when computing the one below it. Continue dividing until the last value written is 1.
| 46 |
| 23 |
| 11 |
| 5 |
| 2 |
| 1 |
3. Write a second column of values next to the first, as a column of binary 1's and 0's. Write a 1 if the number beside it is odd, or a 0 if even.
| 46 | 0 |
| 23 | 1 |
| 11 | 1 |
| 5 | 1 |
| 2 | 0 |
| 1 | 1 |
4. Read the second column from bottom to top, writing out the binary value from left to right:
101110
(which is the binary value for 46)
