Digital logic - Morris Mano

Question

How to multiply two numbers in the given base without converting them into decimals?

$(1230)_4 \text{ and } (23)_4$

Comments

You need to build Times table check this http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/imaiya1.html  it will take more time than converting to Base 10.

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Thank you @Karthik Selvam

Answer 1

In base 4 we can use numbers from 0 to 3.

The rules for multiplication are simple If after any arithmetic operation the numbers go beyond the base (in this case upto 3) then use the idea of carry. 

Consider multiplying 1230 with 3. 

First multiply 3 X 0 = 0 (no problem)

Then multiply 3 X 3 = 9. it is beyond base (not within 0 to 3).  9%4 = 1 which is our result and carry is $\lfloor\frac{9}{4}\rfloor$=2.

When multiplied 3 X 2 = 6 + 2(from carry) = 8 (still beyond) 8%4 = 0 which is our result and carry is $\lfloor\frac{8}{4}\rfloor$=2.

and so on..

Answer is $102210_4$