Final answer:
The binary numbers 1011110111000 and 010000101101001101000 convert to the decimal numbers 7384 and 142696, respectively. Conversion involves assigning powers of two to each position where there is a '1' in the binary number and summing those values.
Step-by-step explanation:
To convert the given binary numbers to decimal, we need to understand that the binary system is based on powers of two. Each digit in a binary number represents a power of two, starting from the rightmost digit which corresponds to 20. Below are the conversions from binary to decimal:
- 1011110111000: This number starts with the least significant bit (the rightmost bit), which corresponds to 20. Starting from the right, each position to the left represents an increasing power of two. So, to convert this to decimal, we add up the values where there is a '1': 212 + 211 + 210 + 27 + 26 + 24 + 23 = 4096 + 2048 + 1024 + 128 + 64 + 16 + 8 = 7384.
- 010000101101001101000: Following the same procedure as above, the decimal equivalent of this binary number can be calculated. The positions with '1' from the rightmost bit are: 217 + 213 + 212 + 28 + 26 + 24 = 131072 + 8192 + 4096 + 256 + 64 + 16 = 142696.
The decimal equivalents for the binary numbers given are 7384 and 142696 respectively.