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April 25th, 2013, 07:52 AM  #1 
Newbie Joined: Apr 2013 Posts: 1 Thanks: 0  Binary Multiplication of two 1024bit numbers
Hi everyone, Is there a efficient way to multiply of two 1024bit binary numbers using fixed sized (for example 32bits) blocks? For simplicity lets take an example of two 8bit numbers. A2 A1 A = 1001 1101 B2 B1 B = 1100 1110 So instead of multiplying AxB I want to do: Step 1: A1xB1 and store the value (=X) Step 2: A2xB2 and store the value (=Y) Step 3: Find some relation between X and Y I cannot think of step 3. So can someone help me with this please. Is it even possible to realize multiplication that way? Regards, Jack 
April 25th, 2013, 10:08 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Binary Multiplication of two 1024bit numbers Quote:
You need A2*A2*16^2 + (A1*B2+A2*B1)*16 + A1*B1. This can be extended to larger numbers in a straightforward way. Keeping track of carries is the hardest part; it's often convenient to use assembly language for this purpose. At 1024 bits you'll probably realize a slight speedup with Karatsuba rather than schoolbook multiplication.  

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