Solve the following
The square root of the binary number 100100
To solve this, we first convert the binary number to decimal form.
100100 in binary is equal to 36 in decimal.
Next, we can find the square root of 36.
√36 = 6
Therefore, the square root of the binary number 100100 is 6.
To find the square root of a binary number, you can convert the binary number to a decimal number and then find its square root.
First, convert the binary number 100100 to decimal:
1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 0 * 2^0
= 32 + 0 + 0 + 4 + 0 + 0
= 36
Now, find the square root of 36:
√36 = 6
So, the square root of the binary number 100100 is 6.
To solve for the square root of the binary number 100100, we need to convert it to decimal first. Here's how to do it:
Step 1: Write down the binary number 100100
Step 2: Assign each digit a corresponding power of 2, starting from the rightmost digit as 2^0 and increasing by 1 for each subsequent digit to the left.
Step 3: Multiply each digit by its corresponding power of 2.
Step 4: Sum all the results from step 3.
Let's go through these steps:
Step 1: The binary number is 100100
Step 2: Assigning powers of 2:
1 0 0 1 0 0
2^5 2^4 2^3 2^2 2^1 2^0
Step 3: Multiply each digit by its corresponding power of 2:
(1 x 2^5) + (0 x 2^4) + (0 x 2^3) + (1 x 2^2) + (0 x 2^1) + (0 x 2^0)
= (1 x 32) + (0 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (0 x 1)
= 32 + 0 + 0 + 4 + 0 + 0
= 36
So the binary number 100100 is equivalent to the decimal number 36.
Now, to find the square root of 36, we can use a calculator or the long division method. Using a calculator, we find that the square root of 36 is exactly 6.
Therefore, the square root of the binary number 100100 is 6.