CODEWITHSUNDEEP
booleanbitboolean-logiccircuit
user93765
user93765

Reputation: 155

Circuit that accept 4-bit number and generate its triple, what does that mean? Can someone give me an example of it?

I have to design a combinational circuit that accepts a 4-bit number and generate its triple, what does it mean? Can someone please give me an example of a specific input and its output so I can understand the question?

If you could give me also any hint for designing this circuit I would be very grateful.

Thank you.

Upvotes: 0

Views: 1595

Answers (2)

Gillespie
Gillespie

Reputation: 6561

You'll want to make a truth table and then derive the combinational logic from either boolean algebra (sum of truths), or from a k-map.

If, for example, the input is 0100 which is decimal 4, then the triple would be 12, or 1100. Since the highest number is 1111 (15), then your output has to be able to represent 45, or 101101 (6 bits).

Hence, you'll have something like:

Input | Output
-----------------
abcd     uvwxyz
0000  | 000000
0001  | 000011
0010  | 000110
0011  | 001001
0100  | 001100
0101  | 001111
0110  | 010010
0111  | 010101
1000  | 011000
1001  | 011011
1010  | 011110
1011  | 100001
1100  | 100100
1101  | 100111
1110  | 101010
1111  | 101101

From that you can build a k-map for each output bit and find the minimum combinational logic required per output bit.

For example, to find the combinational logic for bit u then you would use the following k-map:

         AB
      00 01 11 10
CD 00 0  0  1  0
   01 0  0  1  0
   11 0  0  1  1
   10 0  0  1  0

Which reduces to ACD + AB

Repeat for the other 5 bits (v-z) and you'll have the full combinational logic needed to implement the solution.

Upvotes: 1

Paul R
Paul R

Reputation: 213120

Start with a truth table:

IN              OUT
 0   0 0 0 0     0   0 0 0 0 0 0
 1   0 0 0 1     3   0 0 0 0 1 1
 2   0 0 1 0     6   0 0 0 1 1 0
 3   0 0 1 1     9   0 0 1 0 0 1
 4   0 1 0 0     C   0 0 1 1 0 0
 5   0 1 0 1     F   0 0 1 1 1 1
 6   0 1 1 0    12   0 1 0 0 1 0
 7   0 1 1 1    15   0 1 0 1 0 1
 8   1 0 0 0    18   0 1 1 0 0 0
 9   1 0 0 1    1B   0 1 1 0 1 1
 A   1 0 1 0    1E   0 1 1 1 1 0
 B   1 0 1 1    21   1 0 0 0 0 1
 C   1 1 0 0    24   1 0 0 1 0 0
 D   1 1 0 1    27   1 0 0 1 1 1
 E   1 1 1 0    2A   1 0 1 0 1 0
 F   1 1 1 1    2D   1 0 1 1 0 1

Then use a standard technique such as a Karnaugh Map to deduce the input/output expressions.

Upvotes: 0

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