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

3.4 Apply Q format

  • The value must be converted to a floating-point data type, and then multiplied by the device resolution.
  • If a floating data type needs to be avoided, the fractional temperature data can be discarded using right shift. Alternatively, an integer data type can store mC (milliCelsius) data by taking the product of 1000 before the right shift.
/* C Decode 12-bit Q4 */
unsigned char b1 = 0xff;
unsigned char b2 = 0xf0;

/* combine 8 bit bytes into 16 bit word, 
 apply signed type cast to upper byte */
int x = (signed char) b1 << 8 | b2; 

/* shift to discard unused bits */
int y = x >> 4;

/* Q4 is 2^-4 = 1/16 = 0.0625
 cannot use shift operators on float
 use multiply or divide to create right shift */
float a = y * 0.0625f;

/* discard Q4 bits for a whole number result */
int b = y >> 4;

/* scale by 1000 then shift by Q# to get 
 fractional result without float data type */
int c = y * 1000 >> 4; /* milliCelsius */

/* a is -0.0625, b is -1, and c is -63 */
printf("x:%d y:%d a:%f b:%d c:%d\n",x,y,a,b,c);

/* C Encode 12-bit Q4 */
float in = -0.0625f;

/* Q4 is 2^-4 = 1/16 = 0.0625 
 cannot use shift operators on float
 emulate left shift using multiply */
short int r = in * 16;

/* left shift to create unused/discard bits */
short int s = r << 4;

/* s is 0xFFF0 */
printf("r:%d s:%d sx:%hx",r,s,s);
  • Table 3-7 shows a complete Excel design for 12-bit, Q4. Row 1 illustrates decoding of data received from the sensor while row 2 illustrates encoding data to be sent to the device.
Table 3-7 Excel Example for Q format
ABCDE
11810=HEX2DEC(A1)=IF(B1>=2^15,B1-2^16,B1)=INT(C1*2^-4)=D1*0.0625
2-0.0625=IF(A2<0,A2+2^8,A2)=INT(B2*2^4)=C2*2^4=DEC2HEX(D2)
Table 3-8 Excel Calculation Result for Q format
A B C D E
1 1810 6160 6160 385 24.0625
2 -0.0625 255.9375 4095 65520 FFF0

The following code shows a complete JavaScript and Python decode design for 12-bit, Q4 that can be used to read temperature data.

/* JavaScript */
function decode(x) {return (((x & 0x8000) ? x - 0x10000 : x) >> 4) * 0.0625}
let x = decode(0x1810)
let y = decode(0xFFF0)
/* x is 24.0625 and y is -0.0625 */
# Python
def decode(x): return ((x-0x10000 if (x & 0x8000) else x) >> 4) * 0.0625
x = decode(0x1810)
y = decode(0xFFF0)
# x is 24.0625
# y is -0.0625

The following code shows temperature encoding JavaScript and Python design for 12-bit Q4 that can be used to encode temperature limit or offset settings.

/* JavaScript */
function encode(x) {return ((x < 0 ? x + 0x100 : x) * 16) << 4}
let x = encode(24.0625).toString(16)
let y = encode(-0.0625).toString(16)
/* x is '1810' and y is 'fff0' */
# Python
def encode(x): return int((x+0x100 if (x < 0) else x) * 16) << 4
x = hex(encode(24.0625))
y = hex(encode(-0.0625))
# x is '0x1810'
# y is '0xfff0'