What is $1000000_{16} - 8D6A7B_{16}$ in base 16?
(You do not need to include the subscript 16 in your answer.)
just borrow, making FFFFF<10>. across the top. The result would then be
729585
To subtract these two hexadecimal numbers, we need to align them vertically with their corresponding place values. Let's write down the two numbers:
$1,000,000_{16}$
$- 8D6A7B_{16}$
We need to perform the subtraction digit by digit, starting from the rightmost digit. Since hexadecimal numbers use digits from 0 to 9 and letters A to F, we need to borrow from the left when subtracting a larger digit from a smaller digit.
We get:
$0_{16} - B_{16}$ = (Borrow 1) $16_{10} - 11_{10} = 5_{10}$
$0_{16} - 7_{16}$ = (Borrow 1) $16_{10} - 7_{10} = 9_{10}$
Next:
$0_{16} - 6_{16}$ = (Borrow 1) $16_{10} - 6_{10} = A_{10}$
$0_{16} - A_{16} = -A_{16}$
Next, let's subtract the largest place value digits:
$0_{16} - 6_{16}$ = (Borrow 1) $16_{10} - 6_{10} = A_{10}$
$0_{16} - D_{16} = -D_{16}$
$1_{16} - 8_{16} = -7_{16}$
Finally:
$1_{16} - 8_{16}$ = (Borrow 1) $17_{10} - 8_{10} = F_{10}$
Therefore, $1,000,000_{16} - 8D6A7B_{16} = FFFFFFF5_{16}$
To find the difference between two numbers in base 16, we can subtract each corresponding digit from the second number from the corresponding digit of the first number. If the digit from the second number is greater than the digit from the first number, we'll need to borrow from the next place value.
Let's break down the given expression: $1000000_{16} - 8D6A7B_{16}$.
To subtract the hexadecimal digit D from 0, we need to borrow from the next place value. In base 16, the next place value to the left is worth 16. So, we borrow one from the left, making the 0 a 16.
Now, we have $10_{16} - 8_{16}$. Subtracting 8 from 16 gives us 8.
Next, we subtract A from 6, which requires borrowing from the next place value. So, we convert the 6 into 16 and subtract A from it. In base 16, A is worth 10. Subtracting 10 from 16, we get 6.
Finally, we subtract 7 from 0. Again, we need to borrow from the next place value, so we convert the 0 into 16. Subtracting 7 from 16 gives us 9.
Putting it all together, the difference between $1000000_{16}$ and $8D6A7B_{16}$ is $86A979_{16}$.