Call/WhatsApp: +1 332 209 4094

design and test a three-digit binary-coded-decimal (BCD) adder capable of adding positive and negative BCD numbers

1. Introduction
For this assignment you will design and test a three-digit binary-coded-decimal
(BCD) adder capable of adding positive and negative BCD numbers. The assignment
has a combinational part and a sequential part. You will implement it in two phases;
first the combinational part and next the sequential part.
1.1 Assignment Behavioral Specification
• The BCD adder you design must be capable of adding two three-digit BCD
operands to produce a three-digit sum. Each of the two operands can be either
positive or negative, so the adder must, in effect, be capable of both addition and
subtraction.
• You will represent the operands and sum using 13-bit binary vectors where 12
of the bits are the three 4-bit BCD digits and the 13th bit is a sign bit (0 if the
number is positive and 1 if it is negative). This is essentially a sign-plusmagnitude
representation where the magnitude is represented with the BCD
code.
• The adder should also have a one-bit overflow output signal that is 1 if the
addition results in an overflow (a magnitude that is too big to be represented
with 3 BCD digits) and 0 otherwise. BCD codes and arithmetic are discussed in the
textbook.
1.2 Assignment Organization
The adder is to be organized as three identical digit-adders connected in a ripplecarry
configuration. Each of the digit-adders will be capable of adding two 4-bit BCD
digits and a 1-bit carry/borrow input to produce a 4-bit BCD sum and 1-bit
carry/borrow output. The adder should implement the following general algorithm:
1. The adder checks the signs and relative magnitude of the two operands.
2. If signs are the same, the adder adds the operands and makes the sign of the
result equal the signs of the operands.
3. If the signs differ, then the adder compares the magnitudes of the operands,
subtracts the smaller from the larger, and sets the sign of the result equal to
the sign of the larger. Note that if the result is 0, the sign of the result must be
positive (0 sign bit).
A high-level block diagram for the assignment is given in Figure 1. It shows the main
data flow paths that connect the modules, but does not show the signals that
connect to the control unit. That module will need inputs from the other modules
and will generate control signals for all the modules. Part of the assignment
assignment is to figure out what these control signals should be. The remainder of
this section describes the behavior of the modules in this diagram.
DIGITADD
This is a digit adder that takes two 4-bit BCD digits and a carry/borrow input and
produces a 4-bit BCD sum or difference and a carry/borrow output.
REGUNIT
This module contains two 4-bit registers that hold the input operands for the
DIGITADD module. The BCD input digits must be entered sequentially, one at a time,
into the REGUNIT registers. This unit is also responsible for swapping the operands
when necessary because the available adders can only subtract the B input from the
A input, not the other way around. It is also convenient to add logic to the REGUNIT
to determine which of the input operands is larger (needed to determine if the
operands must be switched). The logic for this should be designed so that when
several REGUNIT modules are connected in series, they will determine which of the
3-digit BCD numbers is larger (or whether they are equal).
CTRLUNIT
This module takes information from the other modules and generates the control
signals for those modules. It must check the signs and magnitudes of the operands
and decide whether to do an addition or subtraction and whether to swap the
operands. It is also responsible for computing the sign of the result.
2. Assignment Implementation
This section gives some more detailed information about how to implement the
modules in the block diagram above. Each of the modules should be implemented as
a VHDL module. We will start with the combinational part of the implementation to
be denoted as Phase I. This implementation will be submitted first.
2.1 PHASE I
A. DIGITADD
Probably the best way to implement the digit adder is by first doing a binary
addition/subtraction and then correcting the sum, if it is outside the range of valid
BCD digits (i.e., greater than 9). The correction can be implemented by adding a
correction value to the intermediate result produced by the first addition or
subtraction. You can implement this with a 4-bit binary adder/subtractor to do the
first addition/subtraction and another binary adder to perform the correction. You
must determine when to do the corrections and what correction values to add. You
will need logic to generate the correction value.
Next, you combine three copies of the digit adder using a structural VHDL module
that uses the other modules as components.
B. Design and Implementation
In this phase, you will develop an algorithm for BCD addition and subtraction and
write a behavioral VHDL module to implement this algorithm. Test the algorithm for
correctness by simulating the VHDL module. You should use high-level VHDL
operations rather than binary logical operations or gate instantiations. For example,
use processes, conditional operations (IF, CASE, etc.), and comments to make it
easy for the reader to understand your algorithm.
C. Testing
It is frequently impractical to test a large circuit by applying all possible input
values. Therefore, it is necessary to select a small subset of test signals that are likely
to catch most of the possible errors. Part of this assignment is to decide how to test
it (i.e., which test inputs to use).
While there is very little theory to help you select test inputs, there are some
guidelines you should consider. For example:
1. Break the assignment into smaller parts and test them exhaustively. For
example, an obvious approach is to test the digit-adder by itself to make sure
it is working before using it in the full adder. (0+0; 0+1; 2+3; 4+5; 5+6; 9+9)
2. Find test signals for the full adder that generate carry signals between stages
and check all the extreme cases and any special cases.
(000+000; 000+001; 123+345; 234+567; 789+777; 999+999)
(000+(-000)); 000+(-001); 345+(-123); 567+(-234); 777+(-789); 999+(-999))
D. Deliverables
Upload to Moodle your (.vhd) files only of all the components that you designed in
addition to the testbench file only for the overall adder. This testbench file will have
the test cases that you selected.
2.2 PHASE II
A. REGUNIT
You should implement the registers in this module so that when the three REGUNIT
modules are connected together, the three A-operand registers form a shift register
and the three B-operand registers form another shift register. These shift registers
should shift from the least significant digit to the most significant digit.
Your input will be loaded to these shift registers, 4 bits at a time at the least
significant part and then shifted to the most significant part. You input the most
significant digit of A and you shift by 4 bits, then you input the most significant digit
of B and you shift by 4 bits, and so on.
You can use multiplexers on the outputs of the registers to swap the two operands.
The logic that checks the relative magnitudes of the operands should take
information from the comparison logic in the previous REGUNIT module and
produce output signals that represent the result of comparing all digits through this
position. These output signals are then passed to the next REGUNIT module. The
output signals of the comparison logic in the last REGUNIT module indicate which of
the full 3-digit operands is largest (or whether or not they are equal).
B. CTLUNIT
This module must contain two flip-flops to hold the signs of the two operands. The
module must also contain logic to use the signs of the two operands and the result of
the magnitude comparison of the operands to compute the sign of the result and to
tell the DIGITADD modules whether to add or subtract.
C. Testing
Repeat the following tests that you performed in Phase I:
• 234 + 567
• 567 + (-234)
• 777 + (-789)
D. Deliverables
Upload to Moodle your (.vhd) files only of all the components that you designed in
addition to the testbench file only for the overall adder. This testbench file will have
the above test cases.

Leave a Reply