SPI with external devices (sensors, displays) in Embedded C - Time & Space Complexity

Time Complexity: SPI with external devices (sensors, displays)

O(n)

Understanding Time Complexity

When using SPI to talk with sensors or displays, it's important to know how long communication takes as data size grows.

We want to see how the time to send or receive data changes when we handle more bytes.

Scenario Under Consideration

Analyze the time complexity of the following SPI data transfer code.

void spi_transfer(uint8_t* data, uint16_t length) {
    for (uint16_t i = 0; i < length; i++) {
        SPI_SendByte(data[i]);
        while (!SPI_TransferComplete());
    }
}
    

This code sends each byte one by one over SPI and waits for the transfer to finish before sending the next.

Identify Repeating Operations

Look at what repeats in the code.

• Primary operation: Sending a byte over SPI and waiting for it to finish.
• How many times: This happens once for each byte in the data array, so exactly length times.

How Execution Grows With Input

As you send more bytes, the total time grows in a straight line with the number of bytes.

Input Size (n)	Approx. Operations
10	10 byte sends and waits
100	100 byte sends and waits
1000	1000 byte sends and waits

Pattern observation: Doubling the number of bytes doubles the total time needed.

Final Time Complexity

Time Complexity: O(n)

This means the time to send data grows directly with the number of bytes you send.

Common Mistake

[X] Wrong: "Sending more bytes over SPI takes the same time as sending just one byte."

[OK] Correct: Each byte requires its own send and wait, so more bytes mean more total time.

Interview Connect

Understanding how SPI communication time grows helps you design efficient embedded systems and answer questions about data transfer speed.

Self-Check

"What if the SPI transfer was done using DMA (Direct Memory Access) instead of waiting for each byte? How would the time complexity change?"