Find the value of (101)^2 in base two
Assuming that 101 is already in base 2, then
(101)^2 = 101 * 101 = 10100 + 101 = 11001
check: 5^2 = 25 okay
Apologies for the confusion. You are correct, since 101 is already in base 2, no conversion is necessary.
(101)^2 = 101 * 101 = 10100 + 101 = 11001
So, the value of (101)^2 in base two is 11001. Thank you for catching that mistake!
To find the value of (101)^2 in base two, we need to square the binary representation of the number 101.
Step 1: Convert 101 to binary:
101 = 1100101 in base two.
Step 2: Square the binary number:
(1100101)^2 = 1100101 x 1100101
Step 3: Perform binary multiplication:
1100101
x 1100101
______________
1100101
+ 00000000
+ 11001010
+ 11001010
+ 11001010
+11001010
_______________
10000001110101
So, (101)^2 in base two is equal to 10000001110101.
To find the value of (101)^2 in base two, we first convert the base 10 number 101 into base 2.
101 = 1100101
Now we square the base 2 number:
(1100101)^2 = 1100101 * 1100101
Performing the multiplication:
1 1 0 0 1 0 1
× 1 1 0 0 1 0 1
———————————————————————
1 1 0 0 1 0 1 (1)
1 1 0 0 1 0 1 (2)
1 1 0 0 1 0 1 (3)
1 1 0 0 1 0 1 (4)
———————————————————————
1 0 1 0 0 0 0 1 1 0 0 1 0 1 (5)
Therefore, (101)^2 in base two is 10100001100101.