Your company is to design a digital hardware subsystem for a 4-Protrusion Code i

Question

Your company is to design a digital hardware subsystem for a 4-Protrusion Code in order to produce printed math books for visually impaired. The user can feel the pattern of protrusions, denoted as A, B, C, D as below, to read a number between 0 and 9 (BCD). The numbers statistically used the most are 0, 1, 5, and 9, which correspond to single-protrusion A, B, C, and D respectively. Double-protrusions are as follows: A & B together denote 2, C & D together denote 3, A & C together denote 4, B & D together denote 8, B & C together denote 6, and finally A & D together denote 7. There never are three or four protrusions in the notation. Derive a minimal SOP (Sum-of-Products) logic implementation for the subsystem to convert BCD code for a given digit to the special code for the visually impaired. You can assume each protrusion in position A-D in the pattern will be represented by 1 if printed, or 0 if not printed, and the input BCD number consists of the digits N_3N_2N_1N_0. Show an implementation of the same logic using NOR gates only (inverters should be implemented using NOR gates).

Explanation / Answer

The Truth Table for N3, N2, N1 and N0 would be as given below:

So The BCD's implementation in Sum of Products would be:

N0 = (A)B(C)(D) + (A)(B)C(D)+(A)(B)(C)D+(A)(B)CD+A(B)(C)D

Considering (A) as A Bar

Similarly

N1= AB(C)(D)+(A)(B)CD+(A)BC(D)+A(B)(C)D

N2= (A)(B)C(D)+A(B)C(D)+(A)BC(D)+A(B)(C)D

N3=(A)(B)(C)D+(A)B(C)D

Also please simplify those expressions.

N3 N2 N1 N0 A B C D 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1

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