# Does splitting random data reduce its security?

Let's say I've got some securely-generated random data I want to encode as words, 32 bits of it. My wordlist is 2048 words, so each word encodes 11 bits of information. I write a routine to pack these 32 bits into the lower 11 bits of 3 16-bit types and zero the upper 5 bits of each. For the last one, I pack in the remaining 10 bits of random data and zero the top 6 instead. I then look each of these up in my wordlist array to get my words. I'd like to use these words.

Here's my question: does what I'm doing reduce the amount of secure randomness I'm encoding in these words? I'd be looking the final word up in a list that's effectively half the size, because the 11th bit is always zero, so is there some "loss of randomness" here? I know this is a little confusing, but I'd appreciate some guidance. I suspect there might be some existing guidance on this, but I'm not sure what to search for to find it and none of my googling has yielded results.

Edit: To clarify, my intuitive guess is that this won't pose a problem, but I'm not comfortable going with that. The closest I've come to rationalizing this is that $$2^{11} \times 2^{11} \times 2^{10} = 2^{32}$$.