Compute .

Question

Compute  .

Quizplus · Accepted Answer

When multiplying two numbers in base 16, we can perform the multiplication as we do in decimal, except that we need to carry over when reaching 16 instead of 10.

First, we write out the two numbers we need to multiply, aligning them with their least significant bits on the right:
```
     11ebfe6a_2cc5_c887_96cc_a36d505fd6c9_TBX8650_11
  *  11ebfe6a_2cc5_ef98_96cc_57fde4a88b8e_TBX8650_11
  -----------------------------------------------------
```

Next, we perform the multiplication as we do in decimal:
```
                      xa      xb      xc      xd      xe      xf      xg
     11ebfe6a_2cc5_c887_96cc_a36d505fd6c9_TBX8650_11
  *  11ebfe6a_2cc5_ef98_96cc_57fde4a88b8e_TBX8650_11
  -----------------------------------------------------
          xx      xx      xx      xx      xx      xx      xx      xa
                  ...
                  ...
                  ...
                  ...
                  ...
                  ...
                  ...
                  ...
                  ...            
```
Note that we only need to compute the values in the first column (xa to xf) to determine the answer to this problem. The rest of the columns are not needed.

In the first column, we have:
```
a * a = a^2
a * e = e * a = d (carry over)
e * e = e^2
e * b = b * e = 9 (carry over)
b * e = e * b = 9 (carry over)
b * f = f * b = 2 (carry over)
f * e = e * f = 8 (carry over)
f * f = f^2
```
Adding up all the values with carry-overs, we get:
```
a^2 + 2d + e^2 + 2*9 + 2*2 + 2*8 + f^2
```
which can be simplified to:
```
a^2 + e^2 + f^2 + 2d + 36
```
Thus, the answer is:
```
11ebfe6a_2cc5_ef9a_96cc_530325dfa615_TBX8650_11
```
which corresponds to choice B.