Finding the Binary Representation of the Given Numbers

To find the number of 1s in the binary representation of (3*4096 15*256 5*16 3), we first need to find the binary representation of each of the given numbers.

- 3*4096:

- 4096 is a power of 2, so its binary representation is simply a 1 followed by 12 zeros: 1000000000000.
- To find the binary representation of 3*4096, we can simply add two binary numbers:
- 1000000000000 (4096)
- 11000000000 (3)
- -------------
- 1001100000000 (12416)

- 15*256:

- 256 is a power of 2, so its binary representation is simply a 1 followed by 8 zeros: 100000000.
- To find the binary representation of 15*256, we can simply add four copies of 256:
- 100000000 (256)
- 100000000 (256)
- 100000000 (256)
- 100000000 (256)
- ----------
- 1111000000000 (3840)

- 5*16:

- 16 is a power of 2, so its binary representation is simply a 1 followed by 4 zeros: 10000.
- To find the binary representation of 5*16, we can simply add four copies of 16:
- 10000 (16)
- 10000 (16)
- 10000 (16)
- 10000 (16)
- ------
- 101000 (80)

- 3:

- 3 is not a power of 2, so we need to find its binary representation using division by 2:
- 3 / 2 = 1 remainder 1
- 1 / 2 = 0 remainder 1
- The binary representation of 3 is therefore 11.

Counting the Number of 1s in the Binary Representation

Now that we have the binary representation of each of the given numbers, we can count the number of 1s in each binary number and add them up to get the total number of 1s in the binary representation of (3*4096 15*256 5*16 3).

- 3*4096:

- The binary representation of 3*4096 is 1001100000000.
- There are 3 1s in this binary representation.

- 15*256:

- The binary representation of 15*256 is 1111000000000.
- There are 6 1s in this binary representation.

- 5*16:

- The binary representation of 5*16 is 101000.
- There are 2 1s in this binary representation.

- 3:

- The binary representation of 3 is 11.
- There are 2 1s in this binary representation.

Adding up the number of 1s in each binary representation,