What is the value of 1310 in binary?

Question

1012

11012

11102

100002

Answer 1

To convert the decimal number 1310 to binary, we can repeatedly divide the number by 2 and keep track of the remainders. Here’s how it’s done:

1. 1310 divided by 2 is 655 with a remainder of 0.
2. 655 divided by 2 is 327 with a remainder of 1.
3. 327 divided by 2 is 163 with a remainder of 1.
4. 163 divided by 2 is 81 with a remainder of 1.
5. 81 divided by 2 is 40 with a remainder of 1.
6. 40 divided by 2 is 20 with a remainder of 0.
7. 20 divided by 2 is 10 with a remainder of 0.
8. 10 divided by 2 is 5 with a remainder of 0.
9. 5 divided by 2 is 2 with a remainder of 1.
10. 2 divided by 2 is 1 with a remainder of 0.
11. 1 divided by 2 is 0 with a remainder of 1.

Now, we write the remainders in reverse order, from the last to the first:

So, \( 1310 \) in binary is \( 10100011110 \).

Now let's review the options you provided:

1. 1012 (not binary)
2. 11012 (not binary)
3. 11102 (not binary)
4. 100002 (not binary)

None of the provided options are correct for representing the binary value of 1310. The correct binary representation is \( 10100011110 \).