Final answer:
The sum of the binary numbers (11101111)₂ and (10111101)₂ was calculated incorrectly as (1101110)₂; the correct sum should be (110101100)₂. The product, however, matches the given product (1011000001110011)₂. Therefore, the overall statement is false.
Step-by-step explanation:
To verify if the summation and multiplication of two binary numbers is correct, we must perform the respective operations on them.
Summation
We add (11101111)2 and (10111101)2:
11101111
+ 10111101
----------
110101100
The sum is (110101100)2, which is different from the given sum (1101110)2. Therefore, the statement about their sum is false.
Multiplication
Next, we multiply (11101111)2 by (10111101)2:
11101111
x 10111101
-----------
11101111
...
+ 00000000 ...
+ 11101111 ...
+ 00000000 ...
+11101111 ...
---------------
1011000001110011
The product matches the given product, so the statement about their product is true.
Since one of the operations (the sum) is incorrect, the overall answer to the statement is B) False.