Convert the base-ten number to a numeral in the indicated base.
19)
15 to base two
19)
______
A)
11110two
B)
111two
C)
1110two
D)
1111two
19 = 16 + 2 + 1
= 2^4 + 0(2^3) + 0(2^2) + 2^1 + 2^0
= 100112
aRgghh!, just realized that 19 was the question #
but let's leave it as another example
15 = 8 + 4 + 2 + 1
= 2^3 + 2^2 + 2^1 + 1
= 11112
To convert a base-ten (decimal) number to a numeral in a different base, such as base two (binary), you can use the process of repeated division by the base.
To convert the number 15 to base two, follow these steps:
1. Start by dividing the base-ten number (15) by the base (2) and note down the remainder. In this case, 15 divided by 2 equals 7 remainder 1.
- Dividend: 15
- Divisor: 2
- Quotient: 7
- Remainder: 1
2. Take the quotient obtained in Step 1 and repeat the process of dividing by the base. In this case, 7 divided by 2 equals 3 remainder 1.
- Dividend: 7
- Divisor: 2
- Quotient: 3
- Remainder: 1
3. Repeat Step 2 with the quotient obtained (3). 3 divided by 2 equals 1 remainder 1.
- Dividend: 3
- Divisor: 2
- Quotient: 1
- Remainder: 1
4. Finally, take the last quotient obtained (1) and the remainders from each step in reverse order to form the base-two numeral. In this case, the remainders were 1, 1, and 1. So the base-two numeral for the base-ten number 15 is 1111.
Therefore, the correct answer is D) 1111two.