• Theory:-

>Excess-3 (XS-3) is a non-weighted code obtained by adding 3 (0011) to each binary-coded decimal (BCD) number.

>It is used to simplify arithmetic operations and error detection, since it avoids all-zero and all-one combinations for valid digits.

>Conversion Principle:
To convert Excess-3 → BCD, simply subtract 3 (0011) from each 4-bit Excess-3 code.

>Process:

• Take the 4-bit Excess-3 input.

• Perform binary subtraction of 0011 (3).

• The result is the corresponding BCD digit

      LOGIC DIAGRAM :

       TRUTH TABLE:

• Boolean Expression:-

B0 = X0'

B1 = X1 ⊕ X0

B2 = X2 ⊕ (X1 + X0)

B3 = X3 ⊕ (X2 (X1 + X0))