many barbaric peoples converted to Islam

Mongolia is predominantly Buddhist (Tibetan I think, but don't quote me on it).

Many of the people they conquered however were already Muslims, particularly through central Asia and the middle east. As happened in China, eventually the Mongols who remained in the conquered territories adopted the culture of their conquests.

The Ottoman empire came after the Mongolians, not before.

Edit… how do I end up with a thumbs down for this? Seriously, I've stated three facts - all of them are correct. Feel free to check them anywhere you like. What justifies a thumbs down? People on this site are just getting moronic about this sort of thing.

because they lacked deductive reasoning, and logic.

They found the truth.
Read the Quran, and you'll convert too.

History has shown that every peoples that has taken over Muslim lands has had a huge increase in people converting to Islam. It's happening in the west today, because they are being introduced to the ideas of Islam by occupying the middle east.

Peace be upon you,

It is true, the Mongol's came and raided Ancient Baghdad, and destroyed the Greatest Libraries of that time.

They eventually did come to Islam, I don't have an explanation as to why their personal reason is, but I do know this

28:56 VERILY, you cannot not guide aright everyone whom you love: but it is God who guides him that wills [to be guided]; [55] and he is fully aware of all who would let themselves be guided. [56]

Some of the footnotes

Note 55 (Quran Ref: 28:56 )

Or: "God guides whomever He wills" - either of these two renderings being syntactically correct. According to several extremely well authenticated Traditions, the above verse relates to the Prophet’s inability to induce his dying uncle Abu Talib, whom he loved dearly and who had loved and protected him throughout his life, to renounce the pagan beliefs of his ancestors and to profess faith in God’s oneness. Influenced by Abu Jahl and other Meccan chieftains, Abu Talib died professing, in his own words, "the creed of Abd al-Muttalib" (Bukhari) or, according to another version (quoted by Tabari), "the creed of my ancestors (al-ashyakh)". However, the Quranic statement " you cannot not guide aright everyone whom you love" has undoubtedly a timeless import as well: It stresses the inadequacy of all human endeavours to "convert" any other person, however loving and loved, to one’s own beliefs, or to prevent him from falling into what one regards as error, unless that person wills to be so guided.(Quran Ref: 28:56 )

Note 56 (Quran Ref: 28:56 )

The above rendering of the expression al-muhtadin conforms to the interpretations offered in this context by many classical commentators - e.g., "those who accept guidance" (Zamakhshari), "everyone who in time would find the right way" (Razi), "those who are prepared (musta’iddin) for it" (Baydawi), "all who deserve guidance" (Ibn Kathir), and so forth. Thus, God’s guidance is but the final act of His grace with which He rewards all who desire to be guided. For a further consideration of this problem, the reader is referred to Zamakhshari’s illuminating remarks quoted in the note 4 on 14:4.(Quran Ref: 28:56 )

Maybe they just seen the way the Muslim's lived, and liked it

Islam is a religion of peace. not politics (lead to wars and terrorism)