Question

Convert the decimal number 80 to binary. Show your work and explain your process in the space below:

a) Provide the correct binary representation.
b) Explain the process of converting 80 to binary.
c) State the decimal equivalent of the binary representation.

Answer 1

To convert the decimal number 80 to binary, divide the number by 2 and write down the remainders until the quotient becomes 0. The binary representation of 80 is 01010000 and its decimal equivalent is 16.

Step-by-step explanation:

To convert the decimal number 80 to binary, you can use the division-by-2 method. Here are the steps:

1. Divide the decimal number by 2.
2. Write down the remainder.
3. Repeat the process with the quotient until the quotient becomes 0.
4. Write down the remainders in reverse order to get the binary representation.

Using this method, let's convert 80 to binary:

• 80 divided by 2 equals 40 with a remainder of 0
• 40 divided by 2 equals 20 with a remainder of 0
• 20 divided by 2 equals 10 with a remainder of 0
• 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

The remainders in reverse order are 01010000, so the binary representation of 80 is 01010000.

The decimal equivalent of the binary representation is calculated by multiplying each binary digit by the corresponding power of 2 and adding the results. In this case, since the leftmost digit is in the 2^6 position, it represents 2^6 * 0 = 0. The second digit from the left is in the 2^4 position, so it represents 2^4 * 1 = 16. Adding all the results, we get 0 + 16 + 0 + 0 + 0 + 0 + 0 + 0 = 16.