SBAA588 April   2024 LM73 , LM75B , LM95071 , TMP100 , TMP101 , TMP102 , TMP103 , TMP104 , TMP107 , TMP1075 , TMP108 , TMP112 , TMP114 , TMP116 , TMP117 , TMP121 , TMP122 , TMP123 , TMP124 , TMP126 , TMP144 , TMP175 , TMP1826 , TMP1827 , TMP275 , TMP400 , TMP401 , TMP411 , TMP421 , TMP422 , TMP423 , TMP431 , TMP432 , TMP435 , TMP451 , TMP461 , TMP464 , TMP468 , TMP4718 , TMP75 , TMP75B , TMP75C

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
    1. 1.1 2's Complement
      1. 1.1.1 2's Complement Traits
    2. 1.2 Q Format
    3. 1.3 Common Temperature Data Format
    4. 1.4 High Accuracy Temperature Data Format
  5. 2Code Examples
    1. 2.1  16 Bits With Q7 Notation
      1. 2.1.1 Properties
      2. 2.1.2 C Code
    2. 2.2  12-bits With Q4 Notation
      1. 2.2.1 Properties
      2. 2.2.2 C Code
    3. 2.3  13-bits With Q4 Notation (EM=1)
      1. 2.3.1 Properties
      2. 2.3.2 C Code
    4. 2.4  13-bits With Q4 Notation
      1. 2.4.1 Properties
      2. 2.4.2 C Code
    5. 2.5  14-bits With Q6 Notation
      1. 2.5.1 Properties
      2. 2.5.2 C Code
    6. 2.6  TMP182x Formats
      1. 2.6.1 Properties
      2. 2.6.2 C Code
    7. 2.7  14-bits with Q5 Notation
      1. 2.7.1 Properties
      2. 2.7.2 C Code
    8. 2.8  8-bits With No Q Notation
      1. 2.8.1 Properties
      2. 2.8.2 C Code
    9. 2.9  11-bits With Q3 Notation
      1. 2.9.1 Properties
      2. 2.9.2 C Code
    10. 2.10 Devices Without 2's Complement
      1. 2.10.1 Properties
      2. 2.10.2 C Code
  6. 3Other Programming Languages
    1. 3.1 Parsing
    2. 3.2 2's Complement
    3. 3.3 Discard Unused Bits
    4. 3.4 Apply Q format
  7. 4Summary
  8. 5References
  9. 6Appendix: Q App Source Code
  10. 7Appendix: Device Summary Table

Abstract

Digital temperature sensors are now an industry-standard due to accuracy and compatibility with various digital interfaces such as I2C, SPI, UART, 1-Wire, PWM, and the emerging I3C MIPI. These plug-and-play devices require no signal conditioning.

At the core, a digital temperature sensor consists of a bias or band-gap reference, integrated or remote temperature sensing transistors, and an integrated analog-to-digital converter (ADC). Note that ADCs in temperature sensors come in different resolutions. For example, a 12-bit ADC output commonly has an LSB of 0.0625°C. After the ADC processes the sensor data, the raw outputs are sent through the digital interface and must be converted into temperature values. These outputs typically use a 2’s complement signed fixed-point representation, which involves placing an implied binary point between two bit locations. This format maintains broad compatibility with various microcontrollers and processors, even those without floating-point support.

This application note provides an overview of the algorithm implementation using fixed-point mathematics. We use the ‘Q Format’ (also known as ‘Q Notation’ or ‘Q Point’) concept for fixed-point representation, to describe and differentiate typical output encodings for temperature sensors. The Qm.n labeling convention represents different temperature sensor output formats and encodings. These concepts are explained at a core quantitative level and then demonstrated using snippets of C code, JavaScript, Python and Microsoft® Excel.