Q format representation

Most of the developers who are working on the multimedia domain are not familiar with the below questionnaire😏.

What is q format?

Why do we require q formats in DSP processors?

Advantages of q format?

Disadvantages of q format?

Once you get to know about q format, then your daily working practice will be quiet easier to understand about code.

Q format is a representation of integers for processing the CPU or DSP.

when a CPU lacks the floating-point unit in a processor then q format is used to enable the rational number processing with hardware arithmetic unit(ALU).

Floating-point operations take so much time and performance-wise also worse when compared with fixed-point. So most companies prefer fixed-point processors only.

We represent fixed-point numbers as Qn format,

Here n represents no.of fractional bits.

Other way of representation is Qm.n

m - no of Integer bits used to represent a decimal number.

n - no of fractional bits used to represents a fractional part 

Q format bits can be any of 8,16,24 or 32. m+n gives the total no.of fractional bits & integer bits.

The maximum positive number that can be represented in for a Q31 format (32-bit variable) is 0x7FFFFFFF which corresponds to 0.9999999. 

The Minimum negative number that can be represented in for a Q31 format is 0x80000000 which corresponds to -0.999999

So the range of Q31 format is [-0.999,0.999]

ex: Float to fixed conversion

5.76 , Here m =  no.of integer bits used to represent the value 5 +  one sign bit. So for my example can fit into Q4.28 format 

5.76 * 2^28 = 1,546,188,226 (0x5C28F5C2)

Let's do some basic operations

1. Addition

a = 5.76 b = 0.76

We can add two floating-point numbers without any conversion, but when you need to add two fixed-point numbers then both should have to be in the same Q format.

a = 5.76 -> Q4.28

b = 0.76 -> Q1.31

a = 5.76 * (2 ^ 28) = 1,546,188,226 (0x5C28F5C2)

b = 0.76 * (2 ^ 31) = 1,632,087,572 (0x6147AE14)

Here a,b are of two different formats. So we need to bring two numbers to the same Q format.

a = Q4.28  

b = (Q1.31 >> 3) = Q4.28 

results = a + b 

           = 0x5C28F5C2+ (0x6147AE14 >> 3)

           = 0x6851Eb84

Conversion of fix to float

result = 0x6851Eb84 / (2 ^ 28) = 6.51

Right shift will increase the no of integer bits & left shift will increase the no of fractional bits.

2. Multiplication

We can multiply two different numbers with different Q-formats.

References :

• https://en.wikipedia.org/wiki/Q_(number_format)

Accepts any suggestions...🙂🙂🙂🙂

Naveen Naik