![]() ![]() The resulting circuit is a purely combinational circuit (the code could have been written linearly, without using a for loop, but it would have been much longer). Note the for loop does not directly describe a circuit – rather, it describes how the circuit components that will do the required shifting and adding are to be assembled. Here, a for loop is used to make the code more compact. Verilog code to implement the double-dabble is shown below. An illustration of the double-dabble algorithm ![]() The figure below illustrates the process (the blue boxes around BCD digits show BCD digits that are >=5, and therefore need 3 to be added). Adding three to any BCD digit greater than five does two things: first, at the next shift, the 3 that was added becomes 6, and that accounts for the difference in binary and BCD codes (BCD uses 10 binary codes, and binary uses 16) and second, adding 3 forces the MSB of the BCD digit to a 1, where it is “carried out” and into the next digit. Since BCD digits cannot exceed nine, a pre-shift number of five or more would result in a post-shift number of ten or more, which cannot be represented. ![]() This works because every left shift multiplies all BCD digits by two. After every shift, all BCD digits are examined, and 3 is added to any BCD digit that is currently 5 or greater. The binary number is left-shifted once for each of its bits, with bits shifted out of the MSB of the binary number and into the LSB of the accumulating BCD number. The “double dabble” algorithm is commonly used to convert a binary number to BCD. Verilog code that converts a binary number to its equivalent decimal representation. module bcd2binĪssign bin = (bcd3 * 10'd1000) + (bcd2* 7'd100) + (bcd1* 4'd10) + bcd0 To convert a binary number to BCD format, we can use an algorithm called Double Dabble. The Verilog code below illustrates converting a 4-digit BCD number to it’s binary equivalent. To find the binary equivalent, each BCD digit is multiplied by its weighted magnitude: 9 x 10^2 + 8 * 10^1 + 7 * 10^0, or 9 * 100 + 8 * 10+ 7 * 1. A case statement should be defined in a always block. Consider the BCD number 987, stored as three 4-bit BCD codes: 1001 for 9 (digit 2), 1000 for 8 (digit 1), and 0111 for 7 (digit 0). In Verilog, if you do not define the base type of a number, it will assume decimal. Each BCD digit in a given number contributes a magnitude equal to the digit multiplied by its weight, and each digit’s weight is equal to 10 raised to the power of the digit’s position in the number. BCD numbers are representations of decimal (base 10) numbers, and like all modern number systems, BCD numbers use positional weighting. ![]()
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