First, to address a problem in your question, you posted it on 26 August 2016, and you say you are asking about a valid Schengen visa, but you say that the visa's expiration date is 23 August 2016. That, of course, means that the visa is no longer valid, so your question is based on a false premise. Namely, your visa is not valid, and you cannot use it to travel.
If we ignore the example dates, though, we can still address the general question, which remains the same in this slightly broader form:
Can I travel to a Schengen country with my old passport that has a valid Schengen visa?
The answer is yes.
The Schengen Borders Code requires certain travelers to hold a valid visa, and to hold a valid passport (or other travel document), but it does not require that the valid visa be contained in the valid travel document. This was confirmed in 2014 by the European Court of Justice in case C-575/12:
On those grounds, the Court (Fourth Chamber) hereby rules:
On a proper construction of Articles 24(1) and 34 of Regulation (EC) No 810/2009 of the European Parliament and of the Council of 13 July 2009 establishing a Community Code on Visas (Visa Code), the cancellation of a travel document by an authority of a third country does not mean that the uniform visa affixed to that document is automatically invalidated.
On a proper construction of Article 5(1) of Regulation (EC) No 562/2006 of the European Parliament and of the Council of 15 March 2006 establishing a Community Code on the rules governing the movement of persons across borders (Schengen Borders Code), as amended by Regulation (EU) No 265/2010 of the European Parliament and of the Council of 25 March 2010, read in conjunction with Article 13(1) of Regulation No 562/2006, the entry of third-country nationals into the territory of Member States is not subject to the condition that, at the border check, the valid visa presented must necessarily be affixed to a valid travel document.
Article 5(1) of Regulation No 562/2006, as amended by Regulation No 265/2010, read in conjunction with Article 13(1) of Regulation No 562/2006, must be interpreted as precluding national legislation, such as that at issue in the main proceedings, which makes the entry of third-country nationals to the territory of the Member State concerned subject to the condition that, at the border check, the valid visa presented must necessarily be affixed to a valid travel document.
The third point basically says that Schengen countries cannot impose an additional requirement that the visa be in a valid travel document.