Question
How to find square root of the binary number 10000
Answers
Answered by
GPT 3.5
To find the square root of the binary number 10000, you can use the long division method. Follow these steps:
Step 1: Group the binary number into pairs from the right, starting with the decimal point. In this case, we have one group: 10.000.
Step 2: Guess the square root of the first group. In this case, the first group is 10, and the square root of 10 is 3.
Step 3: Divide the original number by your guess, 3. The division is: 3 into 10 is 3 remainder 1.
Step 4: Bring down the next pair of digits. In this case, there is no next pair, so bring down a pair of zeros after the remainder. The new dividend becomes 100.
Step 5: Double your previous answer and write it above the new dividend. In this case, 3 x 2 = 6.
Step 6: Determine the largest digit d such that 6d multiplied by d is less than or equal to the dividend. In this case, 60 multiplied by 0 equal 0, so d = 0.
Step 7: Subtract the result of 6d multiplied by d from the dividend, and bring down the next pair of digits (zeros in this case). The new dividend becomes 10000.
Step 8: Finally, repeat steps 5, 6, and 7 until you have brought down all the digits.
In this specific case, since the new dividend is the same as our original number 10000, the division process continues infinitely without reaching a definitive answer. However, by following the steps outlined above, you can calculate as many decimal places of the square root as needed.
Step 1: Group the binary number into pairs from the right, starting with the decimal point. In this case, we have one group: 10.000.
Step 2: Guess the square root of the first group. In this case, the first group is 10, and the square root of 10 is 3.
Step 3: Divide the original number by your guess, 3. The division is: 3 into 10 is 3 remainder 1.
Step 4: Bring down the next pair of digits. In this case, there is no next pair, so bring down a pair of zeros after the remainder. The new dividend becomes 100.
Step 5: Double your previous answer and write it above the new dividend. In this case, 3 x 2 = 6.
Step 6: Determine the largest digit d such that 6d multiplied by d is less than or equal to the dividend. In this case, 60 multiplied by 0 equal 0, so d = 0.
Step 7: Subtract the result of 6d multiplied by d from the dividend, and bring down the next pair of digits (zeros in this case). The new dividend becomes 10000.
Step 8: Finally, repeat steps 5, 6, and 7 until you have brought down all the digits.
In this specific case, since the new dividend is the same as our original number 10000, the division process continues infinitely without reaching a definitive answer. However, by following the steps outlined above, you can calculate as many decimal places of the square root as needed.