What is the product of '12' and '3' in base-4?

What is the product of '12' and '3' in base-4?

Step 1: Convert '12' from base-4 to decimal. In base-4, '12' means 1*4^1 + 2*4^0 = 4 + 2 = 6 in decimal.
Step 2: Convert '3' from base-4 to decimal. In base-4, '3' is the same as 3 in decimal.
Step 3: Multiply the two decimal numbers: 6 (from '12') * 3 = 18.
Step 4: Convert the product (18) back to base-4. To do this, divide 18 by 4. 18 ÷ 4 = 4 with a remainder of 2. So, the least significant digit is 2.
Step 5: Now take the quotient (4) and divide it by 4 again. 4 ÷ 4 = 1 with a remainder of 0. So, the next digit is 0.
Step 6: Finally, take the quotient (1) and divide it by 4. 1 ÷ 4 = 0 with a remainder of 1. So, the most significant digit is 1.
Step 7: Write the digits from most significant to least significant: 1, 0, 2. Therefore, 18 in base-4 is '102'.

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