Excess-3 to BCD Converter

Question

Problem: Excess-3 to BCD Converter. Solve this hands-on electronics task on EWskills.

Accepted Answer

Excess-3 code is generated by adding 0011 to a BCD digit. Therefore, converting Excess-3 back to BCD is equivalent to subtracting:

from the valid Excess-3 input.

For example:

Excess-3 0011 → BCD 0000
Excess-3 1000 → BCD 0101
Excess-3 1100 → BCD 1001

The circuit can be simplified by defining the shared intermediate signal:

N = E1 · E0

The resulting output equations are:

D3 = E3 · (E2 + N)
D2 = (E2 ⊕ N)'
D1 = E1 ⊕ E0
D0 = E0'

Substituting N = E1 · E0:

D3 = E3 · [E2 + (E1 · E0)]
D2 = [E2 ⊕ (E1 · E0)]'
D1 = E1 ⊕ E0
D0 = E0'

Circuit Operation

E1 and E0 are ANDed to generate the shared signal:
```
N = E1 · E0
```
D3 is generated by ORing E2 with N and then ANDing the result with E3.
D2 is generated by XNORing E2 with N.
D1 is generated by XORing E1 and E0.
D0 is generated by inverting E0.

Only valid Excess-3 codes 0011–1100 corresponding to decimal digits 0–9 are required to produce defined BCD outputs. The other six combinations are treated as don't-care conditions.

59. Excess-3 to BCD Converter