[SOLVED] Cse3666 homework 4

1. Design a circuit that takes 4 bits as input and outputs F, which is 1 only when the 4-bit input,
interpreted as an unsigned number, is positive and divisible by 3. The input signals are A, B,
C, and D. D is the least significant bit.
We can start a truth table like the one below and then write a logic equation for F.
We do not simplify the logic expression in this problem.
Row no. A B C D F
0 0 0 0 0 1
1 0 0 0 1 0
2 0 0 1 0 0
3 0 0 1 1 1
…
Implement the circuit in MyHDL. The skeleton code is in q1.py. Compare the truth table
generated by the script with the one constructed manually.
The PDF file needs to include comb() function only.
CSE3666
2. We build a state machine that detects if a binary number of an arbitrary length is divisible by
3. The state machine has three states S0, S1, and S2. The bits in the number are fed into the
machine from left to right, i.e., from the most to the least significant bit, one bit per clock
cycle. The state machine starts from S0. Depending on the current state and the input bit, the
state machine transits from one state to another, as shown in the following diagram. The
numbers in the state names (S0, S1, and S2) are the remainder when we divide by 3 the bits
that the machine has seen. If the state is S0, the bits are divisible by 3.
Implement the state machine in MyHDL. The skeleton code is in hw4q2.py. We can
complete the design in 3 steps. Steps 2 and 3 are combinational circuit.
Step 1. Instantiate a register to keep the state. We leverage the Register block that is provided
in the skeleton code. The input and output signals of the state register have already been
created. You can find an example of instantiating a Register in shift_register.py on the
following page.
cse3666/shift-regsiter.py at master · zhijieshi/cse3666 (github.com)
Step 2. Complete the next_state_logic() function, which generates the state to be saved
in the state register in the next cycle.
Step 3. Complete the z_logic() function, which generates the output signal z, which
indicates whether the number is divisible by 3. The z signal only depends on the current state.
In the PDF file, list your code for each step. In addition, show the output of the program
when eight random bits you choose are sent to the machine. We can specify bits on the
command line. Here is an example where the bit string is 110111.
python hw4q4.py 110111
b | z v
1 | 0 1 # the first bit is the MSB, which is 1
1 | 1 3 # two left most bits 11. It is divisible by 3
0 | 1 6 # now the machine sees three bits 110
1 | 0 13 # and so on
1 | 1 27
1 | 0 55 # all 6 bits are fed to the state machine
CSE3666
Although it is not required, you are encouraged to generate the trace file and observe the
waveforms of signals.
3. Consider the multiplier we have studied. If the delay of the adder is 10 ns, the setup time, the
hold time, and the propagation delay of the registers is 0.2 ns, 0.25 ns, and 0.3 ns,
respectively.
When entering answers in HuskyCT, round answers to the nearest tenth if necessary. For
example, enter 3 for 3, 0.3 for 1/3, and 0.7 for 2/3. Keep the 0 before the decimal point.
a. What is the minimum cycle time for this multiplier to work properly?
b. What is the highest clock rate that this multiplier can run at?
c. If we build a sequential circuit with the same kind of registers and want the circuit run at
1 GHz, what is the maximum delay of the combinational module?
d. If we build sequential circuit with the same kind of registers, what is the highest clock
rate we can achieve?
4. Assume we have built a 5-bit multiplier, based on the design we have discussed, and use it to
calculate 27 * 17. Fill out the following table with bits stored in registers after each step.
Steps Multiplicand Multiplier Product
init
1
2
3
4
5
CSE3666
5. Translate the following C function to RISC-V assembly code. The function converts an
unsigned number into a string that represents the number in decimal. For example, after the
following function call, the string placed in buffer is “3666”.
uint2decstr(buffer, 3666);
Assume the caller has allocated enough space for the string. Skeleton code is in q5.s, where
the function is empty. Clearly mark in comments how each statement is translated into
instructions. The PDF file needs to include the instructions in the function only.
char * uint2decstr(char *s, unsigned int v)
{
unsigned int r;
if (v >= 10) {
s = uint2decstr(s, v / 10);
}
r = v % 10; // remainder
s[0] = ‘0’ + r;
s[1] = 0;
return &s[1]; // return the address of s[1]
}