A programmable address decoder. Works for any address range at any starting
point, *and the base and bound addresses can be changed at runtime*. We do
this with two parallel subtractions to calculate lesser/greater/equal
predicates to check if the input
address lies between the base and bound addresses, inclusively.

This decoder scales to larger address ranges (20 bits or more) without hitting any Verilog implementation vector width limits or requiring long optimization of enormous netlists, as with the static Address Decoder.

For very small address ranges, this decoder will be larger (2 subtractors
instead of a few LUTs). For very large address ranges (e.g. 32 bits or
more), the speed of the arithmetic operations will become a limit, *but it
is unclear if this will be slower than the log _{2}(ADDR_WIDTH) deep
tree of LUT logic* obtainable from a Behavioural Address Decoder.

The base, bound, and input addresses all use the same width, which avoids the need for selecting parts of vectors and makes the enclosing code cleaner and more general.

**Use this implementation if you must use arithmetic circuitry.**
Otherwise, I recommend using the Behavioural Address
Decoder.

`default_nettype none module Address_Decoder_Arithmetic #( parameter ADDR_WIDTH = 0 ) ( input wire [ADDR_WIDTH-1:0] base_addr, input wire [ADDR_WIDTH-1:0] bound_addr, input wire [ADDR_WIDTH-1:0] addr, output reg hit ); initial begin hit = 1'b0; end wire base_or_higher; wire bound_or_lower; Arithmetic_Predicates_Binary #( .WORD_WIDTH (ADDR_WIDTH) ) lower_bound ( .A (addr), .B (base_addr), // verilator lint_off PINCONNECTEMPTY .A_eq_B (), .A_lt_B_unsigned (), .A_lte_B_unsigned (), .A_gt_B_unsigned (), .A_gte_B_unsigned (base_or_higher), .A_lt_B_signed (), .A_lte_B_signed (), .A_gt_B_signed (), .A_gte_B_signed () // verilator lint_on PINCONNECTEMPTY ); Arithmetic_Predicates_Binary #( .WORD_WIDTH (ADDR_WIDTH) ) upper_bound ( .A (addr), .B (bound_addr), // verilator lint_off PINCONNECTEMPTY .A_eq_B (), .A_lt_B_unsigned (), .A_lte_B_unsigned (bound_or_lower), .A_gt_B_unsigned (), .A_gte_B_unsigned (), .A_lt_B_signed (), .A_lte_B_signed (), .A_gt_B_signed (), .A_gte_B_signed () // verilator lint_on PINCONNECTEMPTY ); always @(*) begin hit = (base_or_higher == 1'b1) && (bound_or_lower == 1'b1); end endmodule