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ELEC5160 (Spring, 2024) Dept. of ECE, HKUST Assignment 1--Page 1 of 2
ELEC5160 Digital VLSI System Design and Design Automation
(Spring, 2024)
Assignment 1: (45 marks)
Due Date: 19th March 2023
1. [6 points]
The timing parameters for the following circuit are given below:
tc2q = 1ns
tlogic = 4ns
tsu = 0.5ns
tc2q,cd = 0.1ns
tc2q,logic = 0.15ns
Skew between C1 and C2 = 0.25ns
(a) What is the maximum frequency at which this design can be clocked?
(b) What is the setup slack in this design?
(c) If the skew is changed to -0.25ns, what value of hold time would satisfy this
system?
C1 C2
2. [7 points]
(a) [3 points] Determine expressions for the set-up time, the hold time (with and
without clock overlap), and the clock-to-Q delay for the flip flop shown below.
(b) [3 points] Modify the circuit below to include (i) a synchronous active-high reset
input, (ii) an asynchronous active-low reset input.
D Q
3. [8 points]
Design a 16-bit multiplier with the minimum delay using the modules shown in the
following table. You can only use these modules for the design. You can use multiple
number of each module. Draw the block diagram of your design. How many of the
following modules are used and what is the delay time of your design?
ELEC5160 (Spring, 2024) Dept. of ECE, HKUST Assignment 1--Page 2 of 2
Module Delay (ns)
8-bit multiplier 3.5
1-bit full adder 0.2
n-bit carry-lookahead adder 0.1n+0.5
4. [5 points]
Using carry-save adders, show the step-by-step multiplication of x and y where x is
decimal 21 and y is also decimal 19. Also explain and identify whether you would use
a different type of adder for the final addition step.
5. [6 points]
The following circuit computes the multiplication of an input x with a constant
number (be aware of the minus sign in the figure). Find the binary
representation (0 and 1 only) of the constant number and what is the
corresponding decimal value?
2-7 2-5 2-4 2-1 21 24 2-10 x + + + + + + Out - - - 6. [6 points]
Using the Booth’s multiplication algorithm, show the following multiplication:
100100 * 011000.
7. [4 points]
Complete the timing diagram for the circuit shown below.
Clk
D
D
Q D
Clk
Q
8. [3 points]
A 4-bit ripple carry adder is used to add two numbers, x3x2x1x0 = 1111 and
y3y2y1y0 = 0001. The delay of a full adder is tFA. Assume the delays associated with
generating the sum output and the carry-out are equal. After what time does sum
appear at the output?