Convert 121 base3 to binary
To convert 121 base 3 to binary, we need to convert it to base 10 first and then to binary.
To convert 121 base3 to base 10:
1*(3^2) + 2*(3^1) + 1*(3^0) = 9 + 6 + 1 = 16
Now, let's convert 16 base 10 to binary:
16 divided by 2 equals 8 with a remainder of 0
8 divided by 2 equals 4 with a remainder of 0
4 divided by 2 equals 2 with a remainder of 0
2 divided by 2 equals 1 with a remainder of 0
1 divided by 2 equals 0 with a remainder of 1
Reading the remainders from bottom to top, we get 10000 in binary.
Therefore, 121 base3 is equal to 10000 in binary.
To convert 121 from base 3 to binary, you would first convert it to decimal and then convert the decimal number to binary.
Step 1: Convert base 3 to decimal.
To convert base 3 to decimal, multiply each digit by the corresponding power of 3 and then sum them up.
121base3 = (1 * 3^2) + (2 * 3^1) + (1 * 3^0)
= (1 * 9) + (2 * 3) + (1 * 1)
= 9 + 6 + 1
= 16
Step 2: Convert decimal to binary.
To convert decimal to binary, divide the decimal number successively by 2 and record the remainders from right to left until the quotient becomes zero.
16 ÷ 2 = 8 remainder 0
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Then, read the remainders in reverse order: 10000, which is the binary representation of 16 in base 2.
Therefore, 121 base3 is equivalent to 10000 in binary.
To convert a number from base 3 to binary, you need to follow a two-step process. First, convert the number from base 3 to decimal, and then convert the decimal number to binary.
Step 1: Convert base 3 to decimal
To convert the number 121 from base 3 to decimal, we need to follow the positional notation. Each digit in the base 3 number represents a power of 3.
Start from the rightmost digit of the base 3 number and assign an exponent to each digit. The rightmost digit has an exponent of 0, the next digit has an exponent of 1, the one after that has an exponent of 2, and so on.
For example:
1 * 3^0 + 2 * 3^1 + 1 * 3^2
Simplifying this expression, we get:
1 + 2 * 3 + 1 * 9
Calculating further:
1 + 6 + 9 = 16
So, 121 base 3 is equal to 16 in decimal.
Step 2: Convert decimal to binary
To convert the decimal number 16 to its binary representation, you need to divide the number successively by 2 until the quotient becomes 0, and then read the remainders in reverse order.
Dividing 16 by 2, we get:
16 ÷ 2 = 8 (Quotient) with a remainder of 0
Dividing 8 by 2, we get:
8 ÷ 2 = 4 (Quotient) with a remainder of 0
Dividing 4 by 2, we get:
4 ÷ 2 = 2 (Quotient) with a remainder of 0
Dividing 2 by 2, we get:
2 ÷ 2 = 1 (Quotient) with a remainder of 0
Finally, dividing 1 by 2, we get:
1 ÷ 2 = 0 (Quotient) with a remainder of 1
Now, reading the remainders in reverse order, we get 10000.
Therefore, 121 base 3 is equal to 10000 in binary.