Question

How to determine the square root of a binary number for 9th grade

Answer 1

To determine the square root of a binary number, you can use a process similar to long division. Follow these steps:

1. Start by grouping the binary number into pairs, starting from the right side. If there is an odd number of digits, the leftmost digit will be a single group.

2. Find the largest binary number that, when squared, is less than or equal to the first group of digits. This will be the first digit of the square root.

3. Subtract the squared value obtained from step 2 from the first group of digits and bring down the next group of digits next to it (if any).

4. Double the first digit of the square root obtained in step 2 (call it x) and assume it to be the first digit of a tentative root. Multiply this tentative root by 20 (since we are working in base 2) and choose a digit y such that x * (20 * x + y) is the largest value less than or equal to the number obtained in step 3.

5. Bring down the next group of digits next to the remainder obtained in step 4 (if any).

6. Repeat steps 4 and 5 until you bring down all the groups of digits.

7. The resulting number is the square root of the original binary number.

Here's an example: Let's find the square root of the binary number 1001101.

______________
√1001101 | 1111110
- 100100
_________________________________
011001
- 11001
_________________________________
01001
- 0100
_________________________________
00001

So, the square root of the binary number 1001101 is 111.