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Gatesv

Problem Statement

You are given a four-bit input vector in[3:0]. We want to know some relationships between each bit and its neighbour:

  • out_both: Each bit of this output vector should indicate whether both the corresponding input bit and its neighbour to the left (higher index) are '1'. For example, out_both[2] should indicate if in[2] and in[3] are both 1. Since in[3] has no neighbour to the left, the answer is obvious so we don't need to know out_both[3].
  • out_any: Each bit of this output vector should indicate whether any of the corresponding input bit and its neighbour to the right are '1'. For example, out_any[2] should indicate if either in[2] or in[1] are 1. Since in[0] has no neighbour to the right, the answer is obvious so we don't need to know out_any[0].
  • out_different: Each bit of this output vector should indicate whether the corresponding input bit is different from its neighbour to the left. For example, out_different[2] should indicate if in[2] is different from in[3]. For this part, treat the vector as wrapping around, so in[3]'s neighbour to the left is in[0].
Tip

The both, any, and different outputs use two-input AND, OR, and XOR operations, respectively. Using vectors, this can be done in 3 assign statements.

Official Solution

module top_module (
    input [3:0] in,
    output [2:0] out_both,
    output [3:1] out_any,
    output [3:0] out_different
);

    // Use bitwise operators and part-select to do the entire calculation in one line of code
    // in[3:1] is this vector:                       in[3]  in[2]  in[1]
    // in[2:0] is this vector:                       in[2]  in[1]  in[0]
    // Bitwise-OR produces a 3 bit vector.             |      |      |
    // Assign this 3-bit result to out_any[3:1]:    o_a[3] o_a[2] o_a[1]

    // Thus, each output bit is the OR of the input bit and its neighbour to the right:
    // e.g., out_any[1] = in[1] | in[0];    
    // Notice how this works even for long vectors.
    assign out_any = in[3:1] | in[2:0];

    assign out_both = in[2:0] & in[3:1];

    // XOR 'in' with a vector that is 'in' rotated to the right by 1 position: {in[0], in[3:1]}
    // The rotation is accomplished by using part selects[] and the concatenation operator{}.
    assign out_different = in ^ {in[0], in[3:1]};

endmodule

My Solution

module top_module( 
    input [3:0] in,
    output [2:0] out_both,
    output [3:1] out_any,
    output [3:0] out_different );

    assign out_both = {in[3] & in[2], in[2] & in[1], in[1] & in[0]};
    assign out_any = {in[3] | in[2], in[2] | in[1], in[1] | in[0]};
    assign out_different = {in[0] ^ in[3], in[3] ^ in[2], in[2] ^ in[1], in[1] ^ in[0]};

endmodule