1. **State the problem:** We need to subtract the binary number $(011100)_2$ from $(0101101)_2$ using the complementary method. 2. **Convert both numbers to the same bit length:** - $(0101101)_2$ has 7 bits. - $(011100)_2$ has 6 bits, so we add a leading zero to make it 7 bits: $(0011100)_2$. 3. **Find the 2's complement of the subtrahend $(0011100)_2$:** - First, find the 1's complement by flipping each bit: $$0011100 \to 1100011$$ - Then add 1 to get the 2's complement: $$1100011 + 1 = 1100100$$ 4. **Add the 2's complement of the subtrahend to the minuend:** $$0101101 + 1100100 = 10010001$$ 5. **Check for overflow:** - Since we are working with 7-bit numbers, the 8th bit (leftmost) is an overflow bit. - Discard the overflow bit, leaving us with: $$0010001$$ 6. **Interpret the result:** - The result is positive because there was an overflow bit. - Convert $0010001_2$ to decimal: $$0\times2^6 + 0\times2^5 + 1\times2^4 + 0\times2^3 + 0\times2^2 + 0\times2^1 + 1\times2^0 = 16 + 1 = 17$$ 7. **Verify by decimal subtraction:** - $(0101101)_2 = 45$ decimal - $(011100)_2 = 28$ decimal - $45 - 28 = 17$, which matches our binary result. **Final answer:** $$\boxed{0010001_2}$$ which equals 17 in decimal.