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Digital logic - Morris Mano

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

$(1230)_4 \text{ and } (23)_4$
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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 $102210_4$

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