We started number systems this week and I can convert decimal to binary but going the other way confuses me. How do I turn 101101 into a decimal number step by step?
To convert binary to decimal, multiply each digit by 2 raised to the power of its position, counting from the right starting at 0, then add everything. For 101101, write the position powers from right to left: positions 0,1,2,3,4,5. The digits from right are 1,0,1,1,0,1. So compute 1×2^0 + 0×2^1 + 1×2^2 + 1×2^3 + 0×2^4 + 1×2^5 = 1 + 0 + 4 + 8 + 0 + 32 = 45. So 101101 in binary equals 45 in decimal. A neat shortcut: only add the place values where the bit is 1. Here the 1s sit at place values 1, 4, 8 and 32, and 1+4+8+32 = 45.
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