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

1.2 Q Format

Q format is a method of encoding rational numbers. Typically four or more bits are reserved to express fractional values between 1 and 0. Rational data stored in Q format can be manipulated and stored efficiently without the need for floating point operations that are sometimes prohibited in microcontroller code. In this document, the number following Q refers to the number of fractional bits. Other sources denote the number of integer bits in addition to the fractional bits, as shown in the table, where m is the number of integer bits, including the sign, and n is the number of fractional bits. All sources reviewed agree on a shorthand Qn notation that only includes the n fractional bits after the Q, which is consistent with this document.

Table 1-3 Q Notation Variants
SourceQ FormatQ ExampleExample Detail
This documentQnQ4

12 bits total

8 integer bits including sign

(7 integer bits without sign)

4 fractional bits

Variant 1Qm.nQ8.4
Variant 2 (TI)Q(m-1).nQ7.4
Variant 3 (ARM)Qn.mQ4.8

Q format can also be called a Fixed-point data format. Fixed-point data has a preconfigured resolution where floating point data has a variable resolution. The following table shows the relationship between resolution and bit weight for a chosen Q format. Higher Q formats are possible, but are not employed in temperature sensors today.

Table 1-4 Q format Scaling Factors

Q0

Q1

Q2

Q3

Q4

Q5

Q6

Q7

1

0.5

0.25

0.125

0.0625

0.03125

0.015625

0.0078125

1

1/2

1/4

1/8

1/16

1/32

1/64

1/128

20

2-1

2-2

2-3

2-4

2-5

2-6

2-7

As an example, integer data that is known to be in Q4 format can be converted to the rational Q value by multiplying the data with 0.0625, 1/16 or 2-4 because these values are all equal.