To find out how many calculators the State Board of Education can buy, we divide the total budget by the cost of each calculator.
The total budget is $1,119 and each calculator costs $2.
\[ \text{Number of calculators} = \frac{\text{Total budget}}{\text{Cost of each calculator}} = \frac{1119}{2} = 559.5 \]
Since the State Board cannot buy half a calculator, we round down to the nearest whole number:
\[ \text{Number of calculators bought} = 559 \]
Next, we calculate the total cost for 559 calculators:
\[ \text{Total cost for calculators} = 559 \times 2 = 1118 \]
Now we find out how much money will be left over after buying the calculators:
\[ \text{Money left over} = \text{Total budget} - \text{Total cost for calculators} = 1119 - 1118 = 1 \]
Therefore, the State Board of Education will have \(\boxed{1}\) dollar left over.
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