Perform the following addition in binary notation:

1011.01 + 1.101

Question

Perform the following addition in binary notation:

1011.01 + 1.101

BlackTom AI · Accepted Answer

Align the binary numbers by the radix point and pad the shorter fractional part with zeros:  
1011.010  
+0001.101

Relevant rules: in binary addition 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), and 1+1+1=11 (write 1, carry 1). Also you can verify by converting to decimal.

Step-by-step (fractional bits right to left):
- Rightmost fractional column: 0 + 1 = 1 (carry 0).
- Next fractional column: 1 + 0 = 1 (carry 0).
- Next fractional column (nearest the point): 0 + 1 = 1 (carry 0).

So the fractional result is .111 and there is no carry into the integer part.

Integer part (right to left):
- Least significant bit: 1 + 1 = 0, carry 1.
- Next bit: 1 + 0 + carry 1 = 0, carry 1.
- Next bit: 0 + 0 + carry 1 = 1, carry 0.
- Most significant bit: 1 + 0 + 0 = 1.

So the integer result is 1100.

Combine integer and fractional results: 1100.111

Decimal verification:
- 1011.01₂ = 11 + 0.25 = 11.25
- 1.101₂ = 1 + 0.625 = 1.625
- Sum = 12.875
- 1100.111₂ = 12 + 0.875 = 12.875, matching the sum.

No alternative choices apply here. The correct result is 1100.111, which matches the provided answer.

Perform the following addition in binary notation: 1011.01 + 1.101Short answer

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