An excess-3 to BCD converter is a type of code converter in digital electronics used to translate an XS-3 code into an equivalent binary-coded decimal.

Therefore, an XS-3 to BCD code converter accepts a digital code in XS-3 format and produces an equivalent digital code in BCD format.

The truth table of the XS-3 to BCD code converter is given below −

Excess-3 Code				BCD Code
X₃	X₂	X₁	X₀	B₃	B₂	B₁	B₀
0	0	0	0	X	X	X	X
0	0	0	1	X	X	X	X
0	0	1	0	X	X	X	X
0	0	1	1	0	0	0	0
0	1	0	0	0	0	0	1
0	1	0	1	0	0	1	0
0	1	1	0	0	0	1	1
0	1	1	1	0	1	0	0
1	0	0	0	0	1	0	1
1	0	0	1	0	1	1	0
1	0	1	0	0	1	1	1
1	0	1	1	1	0	0	0
1	1	0	0	1	0	0	1
1	1	0	1	X	X	X	X
1	1	1	0	X	X	X	X
1	1	1	1	X	X	X	X

Now, we will simplify this truth table using K-map method to obtain the Boolean expression for the output bits.

K-Map for BCD Bit B₀

The following figure shows the K-map simplification for the BCD bit B₀.

This K-map gives the following Boolean expression,

$$\mathrm{B_{0} \: = \: \overline{X_{0}}}$$

K-Map for BCD Bit B₁

The following figure shows the K-map simplification for the BCD bit B₁.

This K-map gives the following Boolean expression,

$$\mathrm{B_{1} \: = \: \overline{X_{1}} \: X_{0} \: + \: X_{1} \: X_{0}}$$

K-Map for BCD Bit B₂

The K-map simplification for the BCD bit B₂ is shown below −

The simplification of this K-map gives the following Boolean expression,

$$\mathrm{B_{2} \: = \: \overline{X_{2}} \: \overline{X_{1}} \: + \: \overline{X_{2}} \: \overline{X_{0}} \: + \: X_{2} \: X_{1} \: X_{0}}$$

K-Map for BCD Bit B₃

The K-map simplification for the BCD bit B₃ is shown in the following figure −

By simplifying this K-map, we obtain the following Boolean expression,

$$\mathrm{B_{3} \: = \: X_{3} \: X_{2} \: + \: X_{3} \: X_{1} \: X_{0}}$$

We can use these Boolean expressions to implement the digital logic circuit to perform the XS-3 to BCD conversion.

The logic circuit diagram to convert an XS-3 code into equivalent BCD code i.e., Excess-3 to BCD converter is shown in the following figure −

This is all about some commonly used digital code converters used in various digital electronic applications.

K-Map for BCD Bit B0

K-Map for BCD Bit B1

K-Map for BCD Bit B2

K-Map for BCD Bit B3

K-Map for BCD Bit B₀

K-Map for BCD Bit B₁

K-Map for BCD Bit B₂

K-Map for BCD Bit B₃

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