MCP3008 ADC over SPI in Raspberry Pi - Time & Space Complexity

Time Complexity: MCP3008 ADC over SPI

O(n)

Understanding Time Complexity

When reading analog values using the MCP3008 ADC over SPI on a Raspberry Pi, it's important to understand how the time to get data grows as we read more channels.

We want to know how the number of SPI communication steps changes when we increase the number of channels read.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import spidev

spi = spidev.SpiDev()
spi.open(0, 0)

for channel in range(8):
    adc = spi.xfer2([1, (8 + channel) << 4, 0])
    data = ((adc[1] & 3) << 8) + adc[2]
    print(f"Channel {channel}: {data}")
spi.close()

This code reads analog values from all 8 channels of the MCP3008 ADC by sending SPI commands one channel at a time.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that sends SPI commands to read each channel.
• How many times: Exactly 8 times, once per channel.

How Execution Grows With Input

Each channel read requires one SPI transfer. So if we read more channels, the total SPI transfers increase linearly.

Input Size (n)	Approx. Operations
10	10 SPI transfers
100	100 SPI transfers
1000	1000 SPI transfers

Pattern observation: The number of SPI transfers grows directly in proportion to the number of channels read.

Final Time Complexity

Time Complexity: O(n)

This means the time to read data grows in a straight line as you read more channels.

Common Mistake

[X] Wrong: "Reading multiple channels at once takes the same time as reading one channel."

[OK] Correct: Each channel requires a separate SPI transfer, so reading more channels takes more time, not the same.

Interview Connect

Understanding how hardware communication time grows with input size helps you design efficient data reading loops and manage timing in real projects.

Self-Check

"What if we read only a subset of channels instead of all? How would the time complexity change?"