Final answer:
The decimal equivalent of the binary number (11 0111 1110)2 is 100610, which is obtained by summing the powers of two for the positions where the binary digit is 1.
Step-by-step explanation:
The decimal expansion of the binary number (11 0111 1110)2 is 100610.
To convert a binary number to a decimal number, you start by assigning the place values to each digit, which are powers of 2. Starting from the rightmost digit, the first position has a value of 20, the second 21, and so on, increasing the exponent by one each time as you move to the left. Let's convert the given binary number step by step.
For (11 0111 1110)2, the values from right to left are: 20 (1), 21 (2), 22 (4), 23 (8), 24 (16), 25 (32), 26 (64), 27 (128), 28 (256), and 29 (512). Add these values up where the binary digit is 1. That gives you 512 + 256 + 64 + 32 + 16 + 8 + 4 + 2 = 1006. Thus, (11 0111 1110)2 equals 1006 in decimal notation.