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Start with two bit signed numbers and work your way up from there ... 
That always made me laugh - back in the day when CD players were the Bee's Knees they proudly announced the kit contained a "1 bit DA converter" on the adverts (and the player, normally).
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
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OriginalGriff wrote: when CD players were the Bee's Knees
Ooohhh... and 4X oversampling?
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OriginalGriff wrote: they proudly announced the kit contained a "1 bit DA converter"
Which was entirely correct. Sigma/Delta DA (and AD) converters are indeed 1-bit converters that use crazy oversampling plus noise-shaping to produce an analog output that has the same resolution as a 16 or 24 bit "classical" converter  . The introduction of sigma/delta converters removed a whole class of non-linearity issues with classical converters.
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The question is ambiguous in terms of what "largest negative" means. In a strict mathematical sense, that number is -1. But in an natural language sense, "largest negative" would mean "most negative". For example, when my bank account hits $-500, I owe a larger amount than when its only $-10!
"A little song, a little dance, a little seltzer down your pants"
Chuckles the clown
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Yes, you owe a larger amount - which means you have a lower bank balance!
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
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k5054 wrote: question is ambiguous in terms
I agree.
It needs better term definitions to provide a correct answer.
But I can see that some of the answers above taking it to mean the question is phrased to taken as a trick question and so rather simple.
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I think for a programming forum the question is appropriately precise/clearly worded 
Shame on me, my brain also focused on -Infinity for the largest negative number  
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What you OWE is a positive amount. What your bank account is is a negative amount.
On the other hand, I keep getting a "bill" from a company for -$.01. I have called and talked to them multiple times, and they keep sending me the bill. Just send me the penny. It would be much cheaper.
Brent Hoskisson
Brent
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k5054 wrote: The question is ambiguous in terms
I agree. It lacks rigor. It ought to use the correct mathematical term -- "GREATER THAN".
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This is why I hated math word problems. To me, the "largest negative integer" is -infinity because, for example, -3 is "larger" than -2 on the "negative" scale. "Largeness" to me is ambiguous. But my brain works in weird ways when it comes to converting words into math expressions.
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This certainly implies correctness in the mathematical sense.
The consequence for programmers would then also be:
0 == 0: true
0 > 0 : true
0 < 0 :true
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This was my answer as well. Both the smallest positive and largest negative integers are 0. But I can see the case for both 2 and Infinity.
Brent Hoskisson
Brent
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Mathematically, zero is neither positive or negative ... 
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
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"I reject the premise of the question." -- Leo McGarry
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OriginalGriff wrote: What is the smallest positive integer minus the largest negative integer?
Yeah, I resorted to asking a child.
The smallest positive integer is 1. I can cope with that.
The largest negative integer is infinite. She said infinite negative +1. I am still looking for a way to refute that.
Bastard Programmer from Hell 
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics." -- Some Bell.
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1 is smallest positive integer
-infinity is largest negative integer
1 - (-infinity) is 1 + infinity is
infinity
oops
my coffee cup is overflowing
"A little time, a little trouble, your better day"
Badfinger
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I fell for the same. -1 is larger than -10. The largest negative integer is -1.
Infinity isn't in this game. Made me feel stupid and I loved it 
Bastard Programmer from Hell
"If you just follow the bacon Eddy, wherever it leads you, then you won't have to think about politics." -- Some Bell.
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All depends on one's definition of largest negative integer.
The largest integer that is negative or the largest negative integer compared to all negative integers.
The problem as stated is missing this clarity.
"A little time, a little trouble, your better day"
Badfinger
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Silly me was thinking in Int32.
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The smallest positive integer is either 0 or 1 depending on whether 0 is considered positive or not.
The largest negative integer is -1.
So the answer is 1 or 2.
This is not the intent of question but that is the correct answer given how the question was worded.
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Halfway through my first cup of coffee, this sent me into overthink mode, coming up with everything from infinity to zero. It took some reading of comments to see the correct answer is indeed 2.
Great question Griff.
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You have to define 'largest'.
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I don't - we have dictionaries to do that: 
Quote: largest
Definitions
from the GNU version of the Collaborative International Dictionary of English.
(adjective) Greatest in size of those under consideration.
(adjective) maximal.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
(adjective) Superlative form of large: most large.
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony
"Common sense is so rare these days, it should be classified as a super power" - Random T-shirt
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