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(10.001)₂ − (11.101)₂ by 2's complement

Short answer

Make both numbers equal length. 2's complement of 11.101 is 00.011. Add to 10.001: 10.001+00.011=10.100. No end carry, result is negative. Take 2's complement of sum: invert 10.100 to 01.011, add 0.001 yields 01.100, so answer is -(1.1)₂ = -1.5.

Perform (10.001)₂ - (11.101)₂ using 2's complement method.

To find A−BA - B by 2's complement: add the 2's complement of BB to AA. If an end carry occurs, drop it and the result is positive. If no end carry occurs, the result is negative: take the 2's complement of the sum and put a minus sign.

Make both numbers the same length: A=10.001A = 10.001, B=11.101B = 11.101.

Step 1: 2's complement of B

1’s complement of 11.101=00.010add 1 at LSB=00.010+00.001=00.011\begin{aligned} \text{1's complement of } 11.101 &= 00.010 \\ \text{add 1 at LSB} &= 00.010 + 00.001 = 00.011 \end{aligned}

Step 2: Add to A

   10.001
 + 00.011
 --------
   10.100    (no end carry)

Step 3: No end carry, so the answer is negative. Take the 2's complement of 10.100:

1’s complement=01.011+ 0.001=01.100\begin{aligned} \text{1's complement} &= 01.011 \\ +\,0.001 &= 01.100 \end{aligned}

Answer: (10.001)2−(11.101)2=−(1.1)2(10.001)_2 - (11.101)_2 = -(1.1)_2

Check in decimal: 2.125−3.625=−1.5=−(1.1)22.125 - 3.625 = -1.5 = -(1.1)_2.

✓ Answer checked by Claude Opus 5.5 (high effort)

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