Hexadecimal Subtraction and Borrow Operations Quiz

To solve A₁₆ − 3₁₆, first convert the hexadecimal values to decimal. A in hexadecimal equals 10 in decimal, and 3 remains 3. Thus, 10 - 3 equals 7 in decimal. Therefore, the result of A₁₆ − 3₁₆ is 7.

To solve F₁₆ − 8₁₆, first convert both hexadecimal numbers to decimal. F₁₆ equals 15 in decimal, and 8₁₆ equals 8. Subtracting these gives 15 - 8 = 7 in decimal. Converting back to hexadecimal, the answer remains 7.

To solve 20₁₆ − 15₁₆, convert both numbers from hexadecimal to decimal. 20₁₆ is 32 in decimal, and 15₁₆ is 21 in decimal. Subtracting these gives 32 - 21 = 11. Converting 11 back to hexadecimal results in B, which corresponds to the answer.

In hexadecimal, each digit represents a value from 0 to 15. When you need to borrow during subtraction, you borrow a value of 16 from the next higher digit. This is because the base of the hexadecimal system is 16, making it essential to adjust by this amount when performing calculations.

To subtract 1A₁₆ (which is 26 in decimal) from C₁₆ (which is 12 in decimal), convert both hexadecimal values to decimal. The calculation becomes 12 - 26, resulting in -14. In hexadecimal, -14 is represented as E (which is the two's complement representation of -14 in a 16-bit system).

To solve 35₁₆ − 1D₁₆, first convert the hexadecimal numbers to decimal. 35₁₆ equals 53 in decimal, and 1D₁₆ equals 29 in decimal. Subtracting these gives 53 - 29 = 24. Converting 24 back to hexadecimal results in 18₁₆, which is the final answer.

In the subtraction 23₁₆ − 15₁₆, you need to borrow from the sixteens place because the digit in the ones place (3) is smaller than the digit being subtracted (5). This requires borrowing to perform the subtraction correctly, ensuring that the operation can be completed without resulting in a negative value in that position.

To subtract 1B₁₆ from 40₁₆, convert both numbers to decimal. 40₁₆ equals 64 in decimal, while 1B₁₆ equals 27 in decimal. Subtracting 27 from 64 gives 37 in decimal, which converts back to 25 in hexadecimal (25₁₆). Thus, the result of the subtraction is 25₁₆.

To solve 100₁₆ − 9₁₆, convert both hexadecimal numbers to decimal. 100₁₆ equals 256 in decimal, and 9₁₆ equals 9. Thus, 256 - 9 = 247 in decimal. Converting 247 back to hexadecimal gives F7. Hence, the answer is F7.

In hexadecimal subtraction, when borrowing occurs, the digit from which you borrow decreases by one. This is similar to decimal subtraction, where borrowing reduces the value of the digit by one. In hexadecimal, each digit represents values from 0 to 15, so borrowing still follows the same principle of reducing the value by one.

To solve 5C₁₆ − 2E₁₆, first convert the hexadecimal values to decimal. 5C₁₆ equals 92 in decimal, and 2E₁₆ equals 46. Subtracting these gives 92 - 46 = 46, which converts back to 2E in hexadecimal. Thus, the final result is 2E.

To solve B2₁₆ − 47₁₆, first convert both numbers from base 16 (hexadecimal) to decimal. B2₁₆ equals 178 in decimal, and 47₁₆ equals 71. Subtracting these gives 107 in decimal, which converts back to hexadecimal as 6B. Thus, the result of the subtraction is 6B.