Excess-3 to BCD Code Converter

Quick Overview -

Excess -3 to BCD code Converter / Conversion using K-map.

Solved using K-map.

How to write/make truth table and find output expressions ?

Why first 4 and last 3 output rows are represented ' X ' (don't care conditions).

How to find don't care ? Output Dependencies?

Beginner's Guide to understand Conversion. 

Truth Table -

 

Expression For Solving K-map -

B₃ = Σ_m(11, 12) + d_m(0, 1, 2, 13, 14, 15)

B₂ = Σ_m(7, 8, 9, 10) + d_m(0, 1, 2, 13, 14, 15)

B₁ = Σ_m(5, 6, 9, 10) + d_m(0, 1, 2, 13, 14, 15)

B₀ = Σ_m(4, 6, 8, 10, 12) + d_m(0, 1, 2, 13, 14, 15)

 

K-map for B₃ -

B₃ = Σ_m(11, 12) + d_m(0, 1, 2, 13, 14, 15)

B₃ = E₂E₃ + E₀E₁E₃

 

K-map for B₂ -

B₂ = Σ_m(7, 8, 9, 10) + d_m(0, 1, 2, 13, 14, 15)

B₂ = E₀'E₂' + E₁'E₂' + E₀E₁E₂

 

K-map for B₁ -

B₁ = Σ_m(5, 6, 9, 10) + d_m(0, 1, 2, 13, 14, 15)

B₁ = E₀E₁' + E₀'E₁

 

K-map for B₀ -

B₀ = Σ_m(4, 6, 8, 10, 12) + d_m(0, 1, 2, 13, 14, 15)

B₀ = E₀'

 

Output Boolean Expression -

B₃ = E₂E₃ + E₀E₁E₃

B₂ = E₀'E₂' + E₁'E₂' + E₀E₁E₂

B₁ = E₀E₁' + E₀'E₁

B₀ = E₀'

 

Implementation using Basic Gates -