Packing Bits

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This tutorial describes how to pack 8 bits into a byte using the Pack K Bits block, and how unpack a byte into 8 bits, using the Unpack K Bits block.

The previous tutorial, Converting Data Types, describes the char or byte data type and how to convert between data types. The next tutorial, Streams and Vectors, describes the differences between streams and vectors and how to use them in flowgraphs.

Packing Bits

Packing bits into a byte is useful in representing binary data (as opposed to digitized RF samples) as well when using the modulator blocks: Constellation Modulator, GFSK Mod and OFDM Transmitter. Create a new flowgraph and add the Random Source block to the workspace:

AddRandomSourceToWorkspace.png


Click on Random Source. It is selected when outlined in aqua:

SelectRandomSourceBlock.png


Press the UP or DOWN keys to cycle through the different data types until the byte data type is selected, denoted by the magenta output port color:

ChangeRandomSourceToByte.png


The random source generates bytes with a minimum value of Minimum up to a maximum value of Maximum-1. In this case, Minimum = 0 and Maximum = 2, so it will create binary 0 and 1. A Pack K Bits block is used to parallelize, or pack, multiple bits into a single byte to represent larger binary values.

Add the Throttle, Pack K Bits, Char to Float, and QT GUI Histogram Sink blocks to the flowgraph and connect them:

PackBitsStartingFlowgraph.png

The Pack K Bits block takes K bits and places them into a byte by filling the LSB first.

For this example K=4. The Random Source will generate bit A first. This will be received by Pack K Bits and then stored in the LSB:

[0 0 0 0 0 0 0 A]

The second bit generated by Pack K Bits is B, which is then stored by Pack K Bits according to:

[0 0 0 0 0 0 B A]

Following this trent, the 3rd and 4th bits C and D will then be stored as:

[0 0 0 0 D C B A]

Because K=4 bits have been packed, the byte 0000DCBA will be produced as an output and a new byte will be started. The output value of the byte in decimal (base-10) is:

A*1 + B*2 + C*4 + D*8

For example, if:

  • A=0
  • B=1
  • C=0
  • D=1

the byte would be represented by 00001010 and the decimal value is:

0 + 2 + 0 + 8 = 10

Edit the properties of Pack K Bits:

  • K: 4

Pack4Bits.png


Four bits produces numbers from 2^0=1 to (2^4)-1=15. Edit the top QT GUI Histogram Sink properties and change the following:

  • Title: 4 Bits
  • Number of Bins: 1024
  • Max x-axis: 16

HistogramSink4Bits.png

Four bits produces numbers from 2^0=1 to (2^4)-1=15. Edit the bottom QT GUI Histogram Sink properties and change the following:

  • Title: 1 Bit
  • Number of Bins: 1024
  • Max x-axis: 16

HistogramSink1Bit.png

The flowgraph should now look like the following:

PackBitsFinalFlowgraph.png


Run the flowgraph. The 1 Bit histogram shows values of 0 and 1, while the 4 Bits histogram shows values from 0 to 15:

Histogram4Bits1Bit.png

Unpacking Bits

Unpacking serializes a byte into a string of bits. Add the Unpack K Bits block to the workspace and connect it between the Pack K Bits block and the Char to Float block. Edit the Unpack K Bits block properties:

  • K: 4

UnpackBitsFlowgraph.png


Run the flowgraph. The 1 Bit Histogram shows that the 4-bits have been serialized into values of 0 and 1:

HistogramUnpackBits.png


The unpacking starts with the LSB first and proceeds to the MSB. From the previous example, the Pack K Bits produced a byte with bits 0000DCBA. The Unpack K Bits block then produces an output with bit A first, then B, C and D and the 4 remaining 4 zeros in the byte are ignored. The Unpack K Bits block perfectly undoes the the operation by the Pack K Bits input stream. This can be verified by


The next tutorial, Streams and Vectors, describes the differences between streams and vectors and how to use them in flowgraphs.