# 32 bit multiplication using 16 bit?

Please Note by multiply I don't mean 11 * 11 = 11 But I mean 3*3=9 which is 1001 in binary

I am interested in knowing the following about multiplying numbers:

Let's say I have two 32-bit numbers like this:

A0 * 0B where A,B are 16 bits and 0 is 16 bit zero vector, then How can I perform multiply of these two numbers if I have only 16bit multiplier and 0/16/32 shifter?

For example let's say I have 10101010101010100000000000000000 * 00000000000000001111111101010111 How can I use 16bit multiplier here?

In case I have 0A * 0B then I use what I have to multiply A & B which gives 32 bit answer and I don't need to do anything about it.

In case I have A0 * B0 then I use what I have to multiply A & B which gives 32 bit answer that should appear at the most left so I use shift by 32 bit (the bits moved are filled with zeros)

• Try doing it on paper with 4-bit values. I think that will show you what needs to be done. – Elliot Alderson Dec 26 '20 at 13:17
• @ElliotAlderson already tried that which gave me the answer for the two examples I gave but things didn't work for this specefic case – MrCalc Dec 26 '20 at 13:29
• @ElliotAlderson ok I took more examples and it seems the same as example 2 (Multiply A&B then add 16 zeros to the right) but still not sure about that, can you confirm? – MrCalc Dec 26 '20 at 13:35
• Show us all of your work and ask a specific question. – Elliot Alderson Dec 26 '20 at 13:47
• Your first task is to understand what you are trying to multiply. For example, A0 can be either 160 or -96. Which is it? In other words, binary algorithms for multiplication are different for signed and unsigned algorithms and if you don't define which, you have a very good chance of getting the wrong answer. – Brian Drummond Dec 26 '20 at 14:08

For 16 bit unsigned numbers A to D, where AB and CD are 32 bit numbers formed by concatenation,

AB * CD = (A*C << 32) + ((B*C + A*D) << 16) + B*D

• Hi, Is the following equality true? (BC + AD)<<16 == (BC << 16) + (AD <<16)? – MrCalc Dec 26 '20 at 19:11
• Assuming you correctly handle any potential overflows, yes. – Brian Drummond Dec 26 '20 at 23:02
• Is there something similar when A,B,C,D are 8 bits? – MrCalc Dec 27 '20 at 9:24
• Yes of course; and for decimal digits. You probably learned that one in primary school. – Brian Drummond Dec 27 '20 at 13:34
• what if I have: a∙b=a_(N/2) a_(N/2-1)…a_1∙b_(N/2) b_(N/2-1)…b_1 How to write this as sigma? where each a and b is 16 bits so a in total is 16*N/2 bits – MrCalc Dec 27 '20 at 20:01