Binary Addition with Multi-Bit Carry Chain
Hardware adders form the core of the arithmetic logic unit inside every microprocessor. The logic must account not only for the sum of individual bits but also for the carries that ripple across multiple columns.
The operation below shows the addition of two 8-bit unsigned binary values: A = 01101011 and B = 01011101. The sum is calculated column by column from the least significant bit (position 0) to the most significant bit (position 7).
Trace the carry propagation across all eight bit positions. Determine the final 8-bit sum and identify the behavior of the internal carry bits.
Constraints
- All values are represented as 8-bit binary integers.
- Bit positions are zero-indexed from right to left (LSB is position 0, MSB is position 7).
- The initial carry into position 0 is implicitly 0.
Topics
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