The binary equivalent of 1052 is : 0000 0100 0001 1100

$$(1052)_{10}=(0000~0100~0001~1100)_2$$

To convert the decimal number 1052 to binary, we can repeatedly divide by 2 and keep track of the remainders. Here’s the process:

1. 1052 ÷ 2 = 526, remainder 0
2. 526 ÷ 2 = 263, remainder 0
3. 263 ÷ 2 = 131, remainder 1
4. 131 ÷ 2 = 65, remainder 1
5. 65 ÷ 2 = 32, remainder 1
6. 32 ÷ 2 = 16, remainder 0
7. 16 ÷ 2 = 8, remainder 0
8. 8 ÷ 2 = 4, remainder 0
9. 4 ÷ 2 = 2, remainder 0
10. 2 ÷ 2 = 1, remainder 0
11. 1 ÷ 2 = 0, remainder 1

Now, reading the remainders from the bottom up, we get:

$$(1052)_{10} = (0000~0100~0001~1100)_2$$

So, the binary equivalent of 1052 is : 0000 0100 0001 1100.