Binary Coded Decimal format is a binary encoding of decimal numbers that represents each decimal digit by a fixed binary number. For example, 42 is represented in BCD format by the binary representations of 4 and 2, as shown above. The BCD format is common in electronic systems where numeric digits are displayed, as well as in systems where the rounding and conversion errors introduced by binary floating point representation and arithmetic are undesirable.

We will focus on designing a conversion circuit that converts a BCD formatted number to to a binary formatted number. I chose to detail this direction of conversion as binary to BCD conversion circuits are easily be found by a quick web search.

We will consider two algorithms to perform the conversion, the first being a direct arithmetic approach, and the second an iterative algorithm using a finite state machine with data path (FSMD).

We will be designing for the Basys 2 FPGA board which has 8 input switches. We can use the 8 input switches to encode 2 BCD numbers of 4 bits each. We will therefore concern ourselves with designing a circuit to convert a 2 digit BCD number to a 7 bit binary representation (2⁷ = 128 > 99, the largest 2 digit BCD number we can input).

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