Need Clarification on "Migration" Activity.

Current environment Details:

Platform: Windows 2003 R2 32-bit

Installation Type: Single-Node

EBS Version: 11.5.10.2 32-bit

DB Version: 10.2.0.4 32-bit

My target:

Platform: Linux 64-bit

Installation Type: Single-Node

EBS Version: 11.5.10.2 32-bit

DB Version: 10.2.0.4 64-bit

What I want to ask here is:

How many machines I do require for the whole activity?

I am of the view that I have to go in this way:

Step 1: Platform Migration

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Source Environment i.e. Windows 2003 R2 32-bit (Comprising both "Application" and "Database")

Target Environment i.e. Another box of 64-bit architecture with 64-bit Linux. But after the migration both the "Application" and "Database" will remain of 32-bit.