Convert the following to base 2 and base 10 numbers.
728
To convert 728 to base 2, we divide it by 2 repeatedly until the quotient becomes zero.
728 ÷ 2 = 364 remainder 0
364 ÷ 2 = 182 remainder 0
182 ÷ 2 = 91 remainder 0
91 ÷ 2 = 45 remainder 1
45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
So, 728 in base 2 is 1011011000.
To convert 728 to base 10, it already is in base 10. Therefore, 728 in base 10 is 728.
To convert the number 728 to base 2 and base 10, follow these steps:
1. Base 2 (Binary):
To convert to base 2, divide the number repeatedly by 2, noting the remainder each time until the quotient reaches 0.
728 ÷ 2 = 364 remainder 0
364 ÷ 2 = 182 remainder 0
182 ÷ 2 = 91 remainder 0
91 ÷ 2 = 45 remainder 1
45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Now, from bottom to top, write down the remainders: 1001001000. This is the base 2 representation of 728.
2. Base 10 (Decimal):
The number 728 is already in base 10, so no conversion is necessary.
Therefore, the base 2 representation of 728 is 1001001000, and the base 10 representation remains as 728.