In a base-6 number system, what is the product of '24' and '13'?
Practice Questions
Q1
In a base-6 number system, what is the product of '24' and '13'?
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Questions & Step-by-Step Solutions
In a base-6 number system, what is the product of '24' and '13'?
Step 1: Understand that we are working in base-6. This means that each digit represents a power of 6.
Step 2: Convert '24' from base-6 to decimal. The first digit (2) is in the '6s' place and the second digit (4) is in the '1s' place. So, calculate 2*6 + 4 = 12 + 4 = 16.
Step 3: Convert '13' from base-6 to decimal. The first digit (1) is in the '6s' place and the second digit (3) is in the '1s' place. So, calculate 1*6 + 3 = 6 + 3 = 9.
Step 4: Now, multiply the two decimal numbers we found: 16 (from '24') and 9 (from '13'). So, calculate 16 * 9 = 144.
Step 5: Convert the product (144) back to base-6. To do this, divide 144 by 6 and keep track of the remainders. 144 ÷ 6 = 24 remainder 0, 24 ÷ 6 = 4 remainder 0, 4 ÷ 6 = 0 remainder 4. Reading the remainders from bottom to top gives us '400'.
Step 6: Therefore, the product of '24' and '13' in base-6 is '400'.
