Question

If you only had 4:16 One Hot Decoder and an OR gate with the number of inputs of your choosing, fill in the blanks to explain how you would implement the function x 3 x 2 x 1 ¯ + x 3 ¯ x 2 ¯ x 0 with the hardware you were provided. There are 4 inputs for this function, x 3 − x 0

1) I would choose an OR gate with (2, 3, 4, ..., 16) inputs
2) For input  , I would connect it to input (0, 1, 2, 3) of the decoder
3) For input , I would connect it to input (0, 1, 2, 3) of the decoder
4) For input , I would connect it to input (0, 1, 2, 3) of the decoder
4) For input , I would connect it to input (0, 1, 2, 3) of the decoder

5) For output 0000 of the decoder, (I would not use it, I would connect it to OR gate)
6) For output 0001 of the decoder, (I would not use it, I would connect it to OR gate)
7) For output 0010 of the decoder, (I would not use it, I would connect it to OR gate)
8) For output 0011 of the decoder, (I would not use it, I would connect it to OR gate)
9) For output 0100 of the decoder, (I would not use it, I would connect it to OR gate)
10) For output 0101 of the decoder, (I would not use it, I would connect it to OR gate)
11) For output 0110 of the decoder, (I would not use it, I would connect it to OR gate)
12) For output 0111 of the decoder, (I would not use it, I would connect it to OR gate)
13) For output 1000 of the decoder, (I would not use it, I would connect it to OR gate)
14) For output 1001 of the decoder, (I would not use it, I would connect it to OR gate)
15) For output 1010 of the decoder, (I would not use it, I would connect it to OR gate)
16) For output 1011 of the decoder, (I would not use it, I would connect it to OR gate)
17) For output 1100 of the decoder, (I would not use it, I would connect it to OR gate)
18) For output 1101 of the decoder, (I would not use it, I would connect it to OR gate)
19) For output 1110 of the decoder, (I would not use it, I would connect it to OR gate)
20) For output 1111 of the decoder, (I would not use it, I would connect it to OR gate)

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Answer 1

1) I would choose 4 input OR Gate

2) For input X₃, I would connect it to input 3 of the decoder

3) For input X₂, I would connect it to input 2 of the decoder

4) For input X₁, I would connect it to input 1 of the decoder

5) For input X₀, I would connect it to input 0 of the decoder

6) For output 0000 of the decoder, I would not use it.

7) For output 0001 of the decoder, I would connect it to OR gate

8) For output 0010 of the decoder, I would not use it.

9) For output 0011 of the decoder, I would connect it to OR gate

10) For output 0100 of the decoder, I would not use it.

11) For output 0101 of the decoder, I would not use it.

12) For output 0110 of the decoder, I would not use it.

13) For output 0111 of the decoder, I would not use it.

14) For output 1000 of the decoder, I would not use it.

15) For output 1001 of the decoder, I would not use it.

16) For output 1010 of the decoder, I would not use it.

17) For output 1011 of the decoder, I would not use it.

18) For output 1100 of the decoder, I would connect it to OR gate

19) For output 1101 of the decoder, I would connect it to OR gate.

20) For output 1110 of the decoder, I would not use it.

21) For output 1111 of the decoder, I would not use it.

In the truth table, there are 4 1's in the output. So I chose 4 input OR gate.

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