V22.0436 - Prof. Grishman

Assignment 2: Combinational Circuit -- Decimal Adder

In this assignment, you are to design a two-digit decimal adder, using a binary-coded-decimal representation, and verify the design by simulating it using a popular procedural language such as C or Pascal.

In a binary-coded-decimal (BCD) representation, each decimal digit is represented by four signals, D[0], D[1], D[2], and D[3]. These are interpreted as a binary number, with D[0] being the least significant digit, so that the digit 5 is represented by D[3]=0, D[2]=1, D[1]=0, and D[0]=1. Bit combinations representing values of ten or greater are not valid BCD patterns.

A two-digit decimal number is represented by two sets of four signals: ONES and TENS. A two-digit decimal adder takes two decimal numbers: A-ONES and A-TENS, and B-ONES and B-TENS (16 bits of input in total); it produces a two-digit sum, SUM-ONES and SUM-TENS, and a single CARRY-OUT bit (9 bits total).

The tricky part is to create a decimal adder circuit for a single decimal digit. You can create a circuit directly from the truth table, but there are more straightforward ways. Specifically, you can perform decimal addition of inputs A and B in three steps:

  1. add A and B in a 4-bit binary adder, producing a binary sum BSUM and carry-out COUT1
  2. generate a correction CORR as follows: if BSUM>9, CORR=6 else CORR=0 (remember, you have to do this with a Boolean circuit!); this value will be used to correct digits which are greater than 9
  3. use a second 4-bit binary adder to add BSUM and CORR, producing SUM and a second carry-out COUT2

Finally, you have to produce a carry-out from the decimal digit.

What to Submit:

  1. A design for the circuit, starting from basic logic gates. Don't draw one big circuit --- show the design at several levels. First, create a full-adder from gates; then, a 4-bit adder from full adders; then, a one-digit decimal adder from 4-bit adders and individual gates; finally, a two-digit decimal adder from one-digit adders. This emphasizes the structure of the design and means you have much less to draw.
  2. Determine the propagation delay of the circuit as a multiple of the propagation delay of an individual gate.
  3. Create a simulation of the circuit using a program. Use the same hierarchical approach you used in designing the circuit. Submit a listing of this program.
  4. Write a program to test this circuit. Submit a listing of this program, and the test output. Can you exhaustively test this circuit?

All this should be bundled together and submitted not later than September 29. Late assignments are penalized 10% for each weekday late.