what are the binary representtations
of the following decimal numbers?
17,29,38
To convert decimal numbers to binary, you need to divide the decimal number by 2 repeatedly until the quotient becomes 0. The remainders obtained while performing these divisions will give you the binary representation in reverse order.
Let's calculate the binary representations of the given decimal numbers:
1. Decimal number 17:
- Divide 17 by 2, you get a quotient of 8 and a remainder of 1.
- Divide 8 by 2, you get a quotient of 4 and a remainder of 0.
- Divide 4 by 2, you get a quotient of 2 and a remainder of 0.
- Divide 2 by 2, you get a quotient of 1 and a remainder of 0.
- Divide 1 by 2, you get a quotient of 0 and a remainder of 1.
The binary representation of 17 is therefore 10001.
2. Decimal number 29:
- Divide 29 by 2, you get a quotient of 14 and a remainder of 1.
- Divide 14 by 2, you get a quotient of 7 and a remainder of 0.
- Divide 7 by 2, you get a quotient of 3 and a remainder of 1.
- Divide 3 by 2, you get a quotient of 1 and a remainder of 1.
- Divide 1 by 2, you get a quotient of 0 and a remainder of 1.
The binary representation of 29 is therefore 11101.
3. Decimal number 38:
- Divide 38 by 2, you get a quotient of 19 and a remainder of 0.
- Divide 19 by 2, you get a quotient of 9 and a remainder of 1.
- Divide 9 by 2, you get a quotient of 4 and a remainder of 1.
- Divide 4 by 2, you get a quotient of 2 and a remainder of 0.
- Divide 2 by 2, you get a quotient of 1 and a remainder of 0.
- Divide 1 by 2, you get a quotient of 0 and a remainder of 1.
The binary representation of 38 is therefore 100110.