Convert the base-ten number to a numeral in the indicated base.
40 to base two
To convert a base-ten number to a numeral in a different base, such as base two (binary), follow these steps:
Step 1: Divide the base-ten number by the desired base (in this case, 2) and note down the quotient and the remainder.
40 divided by 2 equals 20 with a remainder of 0.
Step 2: Divide the quotient from the previous step by the base again.
20 divided by 2 equals 10 with a remainder of 0.
Step 3: Repeat the previous step until the quotient becomes zero.
10 divided by 2 equals 5 with a remainder of 0.
5 divided by 2 equals 2 with a remainder of 1.
2 divided by 2 equals 1 with a remainder of 0.
1 divided by 2 equals 0 with a remainder of 1.
Step 4: Reverse the order of the remainders obtained in Step 1 to Step 3.
The remainders in reverse order are 1 0 1 0 0.
Therefore, the base-ten number 40 in base two (binary) is equal to 101000.