Octal Multiplication Techniques Quiz

To convert the octal number 12₈ to decimal, multiply each digit by its corresponding power of 8. The left digit (1) is in the 8¹ place, and the right digit (2) is in the 8⁰ place. Thus, 1×8¹ + 2×8⁰ = 8 + 2 = 10 in decimal.

The octal number system is a base-8 system, meaning it uses eight distinct digits. These digits range from 0 to 7, as there are no digits beyond 7 in this system. Therefore, the valid digits in octal are exclusively 0, 1, 2, 3, 4, 5, 6, and 7.

To multiply 3₈ and 4₈ in octal, first convert them to decimal: 3₈ is 3 and 4₈ is 4. Multiply them to get 12 in decimal. Then, convert 12 back to octal, which is represented as 14₈. However, the multiplication in octal directly yields 12₈. Thus, the answer is 12₈.

To convert the decimal number 16 to octal, divide the number by 8. The quotient is 2 and the remainder is 0. The octal representation is formed by reading the quotient and remainder, resulting in 20₈. Thus, 16 in decimal equals 20 in octal.

To multiply 5₈ (which is 5 in octal) and 6₈ (which is 6 in octal), first convert them to decimal: 5₈ = 5 and 6₈ = 6. Multiplying these gives 30 in decimal. Converting 30 back to octal results in 36₈. However, when considering the octal multiplication directly, 5₈ × 6₈ yields 30₈, as it remains within the octal system.

To convert the octal number 25₈ to decimal, multiply each digit by 8 raised to the power of its position, starting from the right (0). Thus, 2 × 8¹ + 5 × 8⁰ equals 16 + 5, which sums to 21 in decimal.

To multiply 7₈ by 7₈ in octal, first convert 7₈ to decimal, which is 7. Then, calculate 7 × 7 = 49 in decimal. Finally, convert 49 back to octal, resulting in 61₈. Thus, the product of 7₈ × 7₈ in octal is 61₈.

To convert the decimal number 64 to octal, divide 64 by 8. The quotient is 8 and the remainder is 0. Next, divide the quotient (8) by 8, yielding a quotient of 1 and a remainder of 0. Finally, divide 1 by 8, resulting in a quotient of 0 and a remainder of 1. Reading the remainders from bottom to top gives 100₈.

To multiply 4₈ (4 in octal) by 5₈ (5 in octal), first convert them to decimal: 4₈ = 4 and 5₈ = 5. Multiplying gives 4 × 5 = 20 in decimal. Converting 20 back to octal results in 22₈, as 2 × 8¹ + 2 × 8⁰ = 16 + 4 = 20.

To convert the decimal number 100 to octal, divide 100 by 8. The quotient is 12 with a remainder of 4. Then, divide 12 by 8, yielding a quotient of 1 with a remainder of 4. Finally, the quotient of 1 gives us the last digit. Reading the remainders from last to first results in 144 in octal.

To multiply 2₈ and 3₈ in octal, first convert them to decimal: 2₈ is 2 and 3₈ is 3. Multiplying these gives 6 in decimal, which remains 6 when converted back to octal. Thus, the result of 2₈ × 3₈ is 6₈ in octal notation.

To multiply 6₈ and 3₈ in octal, first convert them to decimal: 6₈ is 6 and 3₈ is 3. Multiply these in decimal: 6 × 3 = 18. Now, convert 18 back to octal, which is 22₈. Thus, the product of 6₈ × 3₈ is 22₈ in octal.