Final answer:
The question involves converting binary numbers to decimal by multiplying each bit by 2 raised to its position number and summing the values; the provided answers are 278, 171, 745, and 1024 for the respective binary inputs.
Step-by-step explanation:
The subject of this question involves converting binary numbers to their decimal equivalents. The conversion process uses the base-2 numeral system, where each binary digit (bit) represents an increasing power of 2, starting from the rightmost bit. To convert a binary number to a decimal number, you multiply each bit by 2 raised to the power of its position number (starting from 0), and then sum all the values.
Step-by-Step Conversion
- (a) 100010110
1*(2^8) + 0*(2^7) + 0*(2^6) + 0*(2^5) + 1*(2^4) + 0*(2^3) + 1*(2^2) + 1*(2^1) + 0*(2^0) = 278 - (b) 10101011
1*(2^7) + 0*(2^6) + 1*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0) = 171 - (c) 1011011011
1*(2^9) + 0*(2^8) + 1*(2^7) + 1*(2^6) + 0*(2^5) + 1*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0) = 745 - (d) 10000000000
1*(2^10) + 0*(2^9) + 0*(2^8) + 0*(2^7) + 0*(2^6) + 0*(2^5) + 0*(2^4) + 0*(2^3) + 0*(2^2) + 0*(2^1) + 0*(2^0) = 1024
These calculations give us the decimal equivalents of the binary numbers.