MATLAB: How to show the hex or binary representation for an integer or fixed-point variable in MATLAB

binaryfixed-pointFixed-Point DesignerhexintegerMATLAB

When designing or debugging integer or fixed-point algorithms, there are many cases where it is helpful for the display of values to show their hexidecimal or binary representations. How do I get the display of a variable in the MATLAB Command Window to show my preference of hex or binary?

Best Answer

Use of MATLAB's format command and/or Fixed-Point Designer's fipref object can be use to achieve hex display, binary display, or even octal display.

To see instructions for Simulink click here.

Hex display method 1: format hex

To have the MATLAB Command Window show hex representations of all types of variables, not just integer and fixed-point, the format command can be used.

format hex
a = int8([35,-3])
b = fi(a)

a =
  1×2 int8 row vector
   23   fd
   
b = 
23   fd
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 8
        FractionLength: 0

But keep in mind that this also affects other variables types like double and single.

c = single(pi)

c =
  single
   40490fdb

Hex display method 2: fipref.NumberDisplay

For fixed-point fi-objects, an alternate way to have the MATLAB Command Window show hex representations is to use fipref.

format long % restore format for everything else
fpr = fipref;
fpr.NumberDisplay = 'hex'
d = fi([35,127;-1,-128],1,8,0)

fpr = 
         NumberDisplay: 'hex'
    NumericTypeDisplay: 'full'
         FimathDisplay: 'full'
           LoggingMode: 'Off'
      DataTypeOverride: 'ForceOff'
      
d = 
23   7f
ff   80
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 8
        FractionLength: 0

Note, that fipref does not affect doubles, singles, int8 or any other class, only fi objects.

a = int8([35,-3])
c = single(pi)

a =
  1×2 int8 row vector
    35    -3
    
c =
  single
   3.1415927

Binary display method: fipref.NumberDisplay

For fixed-point fi-objects, fipref can be used to have the MATLAB Command Window show binary, hex, or even octal representations.

fpr = fipref;
fpr.NumberDisplay = 'bin'
d = fi([35,127;-1,-128],1,8,0)

fpr = 
         NumberDisplay: 'bin'
    NumericTypeDisplay: 'full'
         FimathDisplay: 'full'
           LoggingMode: 'Off'
      DataTypeOverride: 'ForceOff'
      
d = 
00100011   01111111
11111111   10000000
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 8
        FractionLength: 0

Quick trick to display binary for MATLAB integers.

To show binary for a MATLAB integer such as int8 or uint64, an easy trick is to use fipref and convert the integer to its fixed-point equivalent. Converting to the fi equivalent is the trivial effort of calling fi()

fpr = fipref;
fpr.NumberDisplay = 'bin';
myInt64Var = int64([14;-1;-5;realmax])
fi(myInt64Var)

myInt64Var =
  4×1 int64 column vector
                     14
                     -1
                     -5
    9223372036854775807
    
ans = 
0000000000000000000000000000000000000000000000000000000000001110
1111111111111111111111111111111111111111111111111111111111111111
1111111111111111111111111111111111111111111111111111111111111011
0111111111111111111111111111111111111111111111111111111111111111
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 64
        FractionLength: 0

In R2017a and later, the conversion of a built-in integer to it's fi equivalent does NOT require a Fixed-Point Designer license. However, it does require that your MATLAB installation include MATLAB Coder OR Simulink OR Fixed-Point Designer.

Note: hex or binary display of fi is stored integer

But aware that the binary or hex display is of the fi object's stored integer value. Recall that for binary-point scaling.

RealWorldValue = StoredIntegerValue * 2^-FractionLength

And, in general

RealWorldValue = StoredIntegerValue * Slope + Bias

y = fi( 35*2^-5, 0, 8, 5 )

y = 
00100011
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 8
        FractionLength: 5

Restoring normal display of values

To restore normal display of values, use MATLAB's format command and fipref.

format long % or short or long g or ...
fpr = fipref;
fpr.NumberDisplay = 'RealWorldValue';
a = int8(37)
b = single(pi)
c = fi( 35*2^-5, 0, 8, 5 )

a =
  int8
   37
b =
  single
   3.1415927
c = 
   1.093750000000000
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 8
        FractionLength: 5

Related Solutions

MATLAB: Some forms of Simulink logging write 64 bit integers as fi objects. Does that mean I need a Fixed-Point Designer license

As of R2017a,

a Fixed-Point Designer license would NOT be required.

As of R2017a,

constructing a fi object whose type is equivalent to MATLAB's 11 built-in numerictypes

double, single, logical, uint8, int8, uint16, int16, uint32, int32, uint64, int64

does not require a Fixed-Point Designer license.

For example, this code

v_u64 = fi( 123, 0, 64, 0)
v_s64 = fi( 123, 1, 64, 0)
v_u32 = fi( 123, 0, 32, 0)
v_s32 = fi( 123, 1, 32, 0)
v_u16 = fi( 123, 0, 16, 0)
v_s16 = fi( 123, 1, 16, 0)
v_u8  = fi( 123, 0,  8, 0)
v_s8  = fi( 123, 1,  8, 0)

would not require a Fixed-Point Designer license.

In R2016b and earlier,

a Fixed-Point Designer license would be required.

This change coincided with another important license change.

In R2016b and earlier,

use of 64 bit integers in Simulink requires a Fixed-Point Designer license.

As of R2017a,

usage of 64 bit integers in Simulink does not require any additional licenses.

FYI:

If you'd like to change a fi object to its built-in MATLAB eqivalent, it's easy to do.

In R2020a and later, you can use utilities castFiToMATLAB

a = fi(123,0,64,0)
a = 
   123
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 64
        FractionLength: 0
>> b = castFiToMATLAB(a)
b =
  uint64
   123

or castFiToInt

> a = fi(123,0,64,0)
a = 
   123
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 64
        FractionLength: 0
>> b = castFiToInt(a)
b =
  uint64
   123

In earlier releases, you can simply cast using the name of the MATLAB class (a.k.a. data type name)

for example

>> a = fi(123,0,64,0)
a = 
   123
          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Unsigned
            WordLength: 64
        FractionLength: 0
>> b = uint64( a )
b =
  uint64
   123

MATLAB: How do the OverflowMode and RoundMode properties interact during fixed point conversion in MATLAB (R2011b)

In the first case, since the 'OverflowMode' is 'wrap', the output will be zero once the limit is exceeded (for WordLength = 8, the limit is 255). Now, consider the Fixed point representation for 0.999:

(0.999*(2^8)) = 255.744

For 'RoundMode' = 'ceil', the final value is 256, which wraps around to zero according to the OverflowMode property. For 'RoundMode' = 'floor', the final value is 255, which gives output = 0.9961 (because 255/256 = 0.9961).

During fixed point conversion, we first need to round off the number to the nearest ceil or floor, and only then check for overflow. This is because, for the overflow check, we need to compare two integers (the input and the maximum integer that can be stored for the given wordlength and fraction length). In order to obtain an integer value for the given floating point input, we first need to perform rounding.

Best Answer

Related Solutions

MATLAB: Some forms of Simulink logging write 64 bit integers as fi objects. Does that mean I need a Fixed-Point Designer license

MATLAB: How do the OverflowMode and RoundMode properties interact during fixed point conversion in MATLAB (R2011b)

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