Design a serial comparator that compares two inputs X and Y,...

Design a serial comparator that compares two inputs $X$ and $Y$, which arrive LSB first. There are three outputs: L, G, and E. L is high if $\mathrm{X}<\mathrm{Y}, \mathrm{G}$ is high if $\mathrm{X}>\mathrm{Y}$, and $\mathrm{E}$ is high if $\mathrm{X}=\mathrm{Y}$.

Key Concepts

Finite State Machine (FSM) for Sequential Comparison

A finite state machine is often employed in serial comparator designs to keep track of intermediate results as bits are compared over time. The FSM transitions between states that represent whether the previously compared bits were equal, or whether one number was found to be greater than the other, thereby determining the final comparison outcome.

Bitwise Comparison and Propagation

Bitwise comparison involves evaluating corresponding bits from two binary numbers to determine their relative magnitudes. In serial comparisons, early bit differences must be propagated through subsequent comparisons, ensuring that once a greater or lesser condition is detected, it is maintained and reflected in the final output.

Serial Comparator

A serial comparator is a digital circuit that compares two binary numbers one bit at a time over consecutive clock cycles. It processes sequential bits rather than handling all bits simultaneously, which is useful in systems where data is received serially or where resource constraints limit parallel processing.

LSB-First Data Processing

When data is received least significant bit (LSB) first, the order of bit arrival affects the comparator’s design. In this scheme, comparisons are delayed until enough bits have been accumulated, and special handling is required to maintain the correct significance of earlier bits during the comparison process.

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