Question

Find the truth table for the outputs Fand G of the hierarchical circuit in Figure 3-46. The symbol shown is for the decoder block in Figure 3-13. 7. 2-to-4 Decoder D2 Decoder D. O FIGURE 3-46 Circuit for Problem 3-7

Answer 1

The Question is solved using following steps :

1. Find Truth table of Decoder 1 to find F

2. Write truth table of F for corresponding inputs

3. Find Truth table of Decoder 2 to find G

4. Write truth table of G for corresponding inputs

Here 'd' is used as don't care input. In the Decoder 2, X is a don't care input,means the value of G doesn't depends upon X,do X is ignored as don't care condition.

The Question is solved using following steps: 1. Find Truth table of Decoder 1 to find F 2. Write truth table of F for corresponding inputs 3. Find Truth table of Decoder 2 to find G 4. Write truth table of G for corresponding inputs Here 'd' is used as don't care input. In the Decoder 2, X is a don't care input,means the value of G doesn't depends upon X,do X is ignored as don't care condition. Basically F = D_0^- D_1^- D_2^- D_3^- [A.B.C.D = A^- + B^- + C^- + D^-] or F = D_0 + D_1 + D_2 + D_3 [where A^-- = A] or, F = D_0 + D_1 + D_2 + D_3 so, for the Decoder -1: so D_0 = w^- x^- y^- = x^- y^- D_1 = w^- x^- y = x^- y D_2 = w^- x y^- = x y^- D_3 = w^- x y = x y therefore F = D_0 + D_1 + D_2 + D_3 or F = x^- y^- + xx^- y + xy^- + xy =

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