Can Trump get to 1237 deligates? Yes, and it may not matter.

The magic number of delegates needed to nominate is 1237 (50% +1). Can Trump get there in pledged delegates? Yes, he has a very good chance, if he suffers no more unexpected losses. However, let's assume he does get there... if he has 1237 or more delegates, he's the nominee - except, he may not be. Here's why; Republican Rule 40 (b);
 

(b) Each candidate for nomination for President of the United States

and Vice President of the United States shall demonstrate the support of a majority of the delegates from each of eight (8) or more states, severally, prior to the presentation of the name of that candidate for nomination. Notwithstanding any other provisions of these rules or any rule of the House of Representatives, to demonstrate the support required of this paragraph a certificate evidencing the affirmative written support of the required number of permanently seated delegates from each of the eight (8) or more states shall have been submitted to the secretary of the convention not later than one (1) hour prior to the placing of the names of candidates for nomination pursuant to this rule and the established order of business

What this actually means is that in order for a name to be places in nomination, a candidate must have the delegates from at least 8 states certify that the candidate has a majority (50% +1) of that states delegates. Trump has won more than 8 states by enough to have majority control of the deligates from that state, BUT, the key is "a certificate evidencing the affirmative written support...". Delegates pledged to Trump are pledged to vote for him on the first ballot, but they are not pledged to provide rule 40 (b) certification. Therefor, a few delegates in key states could simply decline to so certify, and having 1237 delegates becomes irrelevant because the candidate's name can't be placed in nomination. Cruz has seemed to focus particular attention on states like South Carolina (where Trump won all the delegates) that Trump needs as part of meeting rule 40 (b), which makes me suspect this particular play might be in his arsenal if Trump reaches 1237 delegates.

However, it's been said that this rule, passed in 2012, can be changed. It can, by the delegates on the rules committee.  To do so would requite the support of the Secretary of the Convention, who is, this year, Speaker of the House Paul Ryan. What it would not actually require is the support of a majority of delegates on the rules committee (this is true of any rule) because it can be passed by voice vote. A voice vote is simply the yeas and nays shouting out their vote, and then the convention secretary (Ryan) decides which side has more, in his opinion alone - no matter the actual result. In case anyone thinks this (a convention secretary ignoring the actual result to get what he wants) is far-fetched, I'll mention that this is exactly how rule 40 (b) was passed in the first place in 2012; the convention secretary was speaker of the house John Bohner, and here's the video;
   https://www.youtube.com/watch?v=77W5OKStO5s
Note that the teleprompter had the results BEFORE Boehner ruled on the result of the vote. Noted also that the "no" vote seemed louder.

So, what can we really expect from the convention? My guess; Cruz will do all he can to stop Trump, even if Trump has the needed 1237 delegates. Once Cruz has done so, Paul Ryan will lift rule 40 (b), and then Cruz will find himself in a very interesting position; while some delegates are loyal to him, a great many are not; they are loyal to their state party bosses - and Cruz will find his own delegate totals shrinking as some of his delegates, and some of Trump's, defect to other candidates.  Paul Ryan himself may be one, though he's denied it just as vociferously as he denied he was running for Speaker of the House. Other possibilities are failed cantidates such as Jeb Bush, Marco Rubio, or John Kasich - I note that Rubio wrote letters to the sates in which he'd won deligates asking that they remain committed to him.

My prediction, then, is that if this goes past the first ballot, the nominee will be neither Trump or Cruz. Instead, we'll end up with a party establishment loyalist of some sort - and a landslide loss in November.