Exhibit 5.1

Gibson, Dunn & Crutcher LLP   1881 Page Mill Road Palo Alto, CA 94304-1211 Tel 650.849.5300 www.gibsondunn.com

August 28, 2012

Applied Micro Circuits Corporation

215 Moffett Park Drive

Sunnyvale, CA 94089

Re: Applied Micro Circuits Corporation Registration Statement on Form S-8

Ladies and Gentlemen:

We have examined the Registration Statement on Form S-8 (the “Registration Statement”), of Applied Micro Circuits Corporation, a Delaware corporation (the “Company”), to be filed with the Securities and Exchange Commission (the “Commission”) on or about August 28, 2012 pursuant to the Securities Act of 1933, as amended (the “Securities Act”), in connection with the registration by the Company of (a) 8,670,334 shares (the “Plan Shares”) of the Company’s common stock, par value $0.01 per share, to be offered pursuant to the Veloce Technologies, Inc. Amended and Restated 2009 Stock Incentive Plan (the “2009 Plan”), (b) 4,340,233 shares (the “Bonus Shares” together with the Plan Shares, the “Shares”) of Common Stock issuable upon the settlement of outstanding awards granted under the Veloce Technologies, Inc. Employee Bonus Plan (the “Bonus Plan” together with the 2009 Plan, the “Assumed Plans”), and (c) 1,800,000 shares of Common Stock to be offered pursuant to the Company’s 2012 Employee Stock Purchase Plan (the “ESPP” together with the Assumed Plans, the “Plans”). Each of the Assumed Plans, along with the outstanding awards under the Bonus Plan, were assumed by the Company pursuant to the Agreement and Plan of Merger, dated May 17, 2009, by and among the Company, Espresso Acquisition Corporation, Veloce Technologies, Inc. and Jeffrey Harrell, as stockholders’ representative (collectively, the “Parties”), as amended by amendment No. 2 to Agreement and Plan of Merger, dated April 5, 2012, by and among the Parties and Veloce Technologies, LLC.

We have examined the originals, or photostatic or certified copies, of such records of the Company and certificates of officers of the Company and of public officials and such other documents as we have deemed relevant and necessary as the basis for the opinions set forth below. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies. We have also assumed that there are no agreements or understandings between or among the Company and any participants in the Plans that would expand, modify or otherwise affect the terms of the Plans or the respective rights or obligations of the participants thereunder. Finally, we have assumed the accuracy of all other information provided to us by the Company during the course of our investigations, on which we have relied in issuing the opinion expressed below.

Based upon the foregoing examination and in reliance thereon, and subject to the qualifications, assumptions and limitations stated herein and in reliance on the statements of fact contained in the documents that we have examined, we are of the opinion that the Shares, when issued and sold in accordance with the terms set forth in the Plans and against payment therefor, and when the Registration Statement has become effective under the Securities Act, will be validly issued, fully paid and non-assessable.

We render no opinion herein as to matters involving the laws of any jurisdiction other than the Delaware General Corporation Law (the “DGCL”). This opinion is limited to the effect of the current state of the DGCL and the facts as they currently exist. We assume no obligation to revise or supplement this opinion in the event of future changes in such law or the interpretations thereof or such facts.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations of the Commission.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP