1-bit binary addition (sum and carry): Compute 1 + 1 and report the sum and carry.
Digital Electronics
Digital Arithmetic Operations and Circuits
Difficulty: Easy
Choose an option
-
Asum = 1 carry = 1
-
Bsum = 0 carry = 0
-
Csum = 1 carry = 0
-
Dsum = 0 carry = 1
-
Esum = 0 carry = X
Answer
Correct Answer: sum = 0 carry = 1
Explanation
Introduction / Context:Single-bit addition defines the core behavior of ripple and CLA adders. Adding two ones produces a sum bit and a carry to the next stage.
Given Data / Assumptions:
- a = 1, b = 1, carry_in = 0.
- Standard full-adder equations.
Concept / Approach:Sum = a xor b xor carry_in; Carry_out = majority(a, b, carry_in). With a=b=1 and carry_in=0, Sum=0 and Carry_out=1.
Step-by-Step Solution:
Compute sum: 1 xor 1 xor 0 = 0.Compute carry: majority(1,1,0) = 1.Report (sum, carry) = (0, 1).Verification / Alternative check:Truth table of a half adder shows 1+1 → sum 0, carry 1.
Why Other Options Are Wrong:
Any combination other than sum 0, carry 1 contradicts equations.Common Pitfalls:Forgetting to include the carry signal when moving to the next bit.
Final Answer:sum = 0 carry = 1