Conversion between number systems

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Conversion between number systems

Relation between Dual code and Hexadecimal code:

When we compare the binary coded number ‘1100 1101’ with the number in hex ‘CD’, we recognize, that always 4 binary digits build a hex digit. The reason is that with 4 binary numbers exactly 16 numbers can be displayed (from 0 to F).

Relation between Dual code and Hexadecimal code

Relation between Dual code and Hexadecimal code


Decimal to Binary

Decimal numbers can be converted to binary by repeated division of the number by 2 while recording the remainder. We explain it with an example:

From Decimal to Binary

From Decimal to Binary


Decimal to Hexadecimal

Decimal numbers can be converted to Hex by repeated division of the number by 16 while recording the remainder. Let’s take an example to see how this works.

Decimal to Hexadecimal

Decimal to Hexadecimal


Exercises

A DIL (Dual In-Line) switch is used to set the binary bus address of an electronic module. The first slide switch on the left stands for the LSP (least significant bit) and the last slide switch on the right for the MSB (most significant bit) of the dual number.

The address 82 (Dec) should now be set. In which picture was the DIL switch correctly set to this address 82 (Dec)?

Exercise - Number systems - Binary numbers

Exercise – Number systems – Binary numbers