Double Dabble

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In the previous exercise, we built circuits that calculate in Binary.

  • Binary: 1111
  • Human Readable: 15

To display binary values (like on a 7-segment display), we need conversion. The algorithm we use for this is called Double Dabble (or Shift-Add-3).

1) The Double Dabble Algorithm

How it Works

We take our binary number and shift it into "bins" representing our decimal digits (Ones, Tens, Hundreds). However, a 4-bit binary digit can go up to 15, but a decimal digit can only go up to 9.

  • The Rule: If any 4-bit BCD column is 5 or greater, we must add 3 to it before the next shift.

Why Add 3? When converting binary to decimal, we need to ensure that each 4-bit group (BCD digit) stays valid (0-9). If a group becomes \ge 5, we add 3. This correction prevents invalid BCD digits (like 1010=10).

Example: Converting 15 (1111)

Let's trace the conversion of the binary number 1111.

Operation Tens Column Ones Column Remaining Binary Note
Start 0000 0000 1111 Initial State
Shift 1 0000 0001 111
Shift 2 0000 0011 11 Value is 3 (<5), keep going.
Shift 3 0000 0111 1 Value is 7 (\ge5)! ADD 3.
Add 3 0000 1010 1 7 + 3 = 10 (1010)
Shift 4 0001 0101 - The '1' from Ones shifts to Tens.
Result 1 5 15

In the Double Dabble algorithm, when do you add 3 to a column?

2) Implementing the Double Dabble Algorithm

The 74185 Binary-to-BCD Converter

This is an example of an IC which implements the logic of this algorithm. We will be using it as a reference for the intended behaviour.

Figure 1: The 74185 IC. Inputs are pure binary (pins 10, 11, 12, 13, 14), and outputs are BCD (pins 1, 2, 3, 4, 5, 6). Note that "enable" (pin 15) must be grounded for the IC to function.
  • Function: Converts 6-bit Binary input into 6-bit BCD output.
  • Cascading: You can connect multiple 74185 chips together to convert larger numbers (8-bit, 16-bit, etc.).
  • Usage: Simply connect your binary source (switches or adder output) to the Binary Inputs and take the BCD Outputs to the next stage.
  • Note: In the inputs, A is the least significant bit and E is the most significant bit, and for the output, Y1 is least significant and Y6 is most significant. 74185 does not use pins Y7 and Y8, and those are internally unconnected

Refer to this to see how to connect the inputs and outputs. Note that the datasheet is for two different ICs, 74184 and 74185, and that the input/output diagrams for 74185 are on pages 7 and 8.

Use this link if the file does not open below:

Refer to Figs. 4 and 5 above for up to 8 bits of input. Note that the least significant input bit always goes directly to the output, bypassing the IC.

An example implementation

Inputs: B_0,B_1,B_2,B_3,B_4,B_5

Outputs: Y_0,Y_1,Y_2,Y_3,Y_4,Y_5,Y_6

Detector (Comparator and AND): This checks at the 4-bit digit and outputs “HIGH” if the digit is 5 or more. A digit in binary is 5 or more if its 8’s bit is HIGH, or if the 4's bit is HIGH along with either the 2's bit or the 1's bit being HIGH

\big[A \ge 5\big]\equiv \big[A_8 OR (A_4 AND (A_2 OR A_1))\big]

Adder: The detector’s yes/no signal is wired into the two least significant bits of the adder’s second input (input B), so the adder adds a correction of 3 when the digit is 5 or more, and 0 otherwise.

This is cascaded three times to give the conversion from 6 binary bits to 2 BCD digits (going from 00 to 63).

3) Building the double-dabble circuit

Components needed

  • 1× 8-bit DIP switch
  • 2× 7-segment common cathode LED
  • 3× 74283 (4-bit adder) IC
  • 2× 7448 (BCD to 7-segment converter) IC
  • 1× 7408 (AND gates) IC
  • 2× 7432 (OR gates) IC
  • 8× 220Ω resistors

Schematic

Final Submission

Upload a video (15 seconds) showing your full conversion circuit. Set the input switches to '111111' and clearly show the display reading '63'. Then switch to '000000' to show it clearing to '00'.
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In this module's project, you'll make a simple 4-bit calculator that can add two binary numbers.