Provide answers to the following questions:

1. Convert the following binary numbers to hexadecimal and to decimal:
   • 10101,
   • 01

How many times the decimal answer in (b) is larger than that in (a)? Explain why.

2. Do the following conversion problems:
   • Convert decimal 37.875 to binary.
   • Calculate the binary equivalent of 1/7 out to eight places. Then convert from binary to decimal. How close is the result to 1/7?
   • Convert the binary result in (b) into hexadecimal. Then convert the result to decimal. Is the answer the same?
3. Represent the decimal number 7814 in (a) BCD, (b) excess3 code, (c) 2421 code, and (d) 6311 code.
4. We can perform logical operations on strings of bits by considering each pair of corresponding bits separately (called bitwise operation). Given two eightbit strings A = 10110101 and B = 00011100, evaluate the eightbit result after the following logical operations: (a) AND (b) OR (c) XOR (d) NOT A (e) NOT B (f) NAND (g) NOR
5. Simplify the following Boolean expressions to a minimum or the indicated number of literals:
   1. (a + b + c)(ab+ c)
   2. abc + abc + abc + abc
   3. (a + c)(a+ b + c)(a+ b+ c)
   4. ABD + ABCD+ ABCD to two literals
6. Given the Boolean functions F1 and F2 , show that
   1. The Boolean function E = F1 + F2 contains the sum of the minterms of

F1 and F2

1. The Boolean function G = F1 F2 contains only the minterms that are common to F1 and F2 .

7. Convert each of the following to the other canonical form.
   1. F(x, y, z) = (1, 3, 5, 7)
   2. F(A, B, C, D) = (3, 5, 8, 11, 13, 15)
8. Write the following Boolean expressions in:
   1. (b + d)(a+ b+ c)(a + c) SOP form
   2. ab + ac+ bc POS form
9. Determine whether the following Boolean equation is true or false.
   1. yz + yz + xz = x+ xz
   2. xy+ xz+ yz = yz + xy + xz
10. Simplify the following Boolean functions, using Karnaugh maps:
    1. F (w, x, y, z) = (11, 12, 13, 14, 15)
    2. F (w, x, y, z) = (8, 10, 12, 13, 14)
11. Simplify the following Boolean functions and expressions, using four-variable maps:
    1. F (A, B, C, D) = (2, 3, 6, 7, 12, 13, 14)
    2. F (w, x, y, z) = (1, 3, 4, 5, 6, 7, 9, 11, 13, 15)
    3. ABCD + ABC + CD + BD
    4. ABCD + BCD + ACD + ABCD + ACD
12. Implement the following logical functions with two-level NAND gate circuits.

Write down the simplification process.

1. F(A, B, C, D) = AD + BCD+ ABC + ABCD
2. F(A, B, C, D) = ABCD + CD + ACD
3. F(A, B, C, D)= (A+ C+ D)(A+ C)(C+ D)
4. F(A, B, C, D) = A+ AB + BC + ACD

PART 2: DIGITAL DESIGN LAB

INTRODUCTION

In this lab, you are required to use Vivado 2017.4 and Minisys/EGO1 Practice platform (xilinx FPGA chip artix 7 inside) to design a combinational logic circuit and test it.

PREAMBLE

Before working on the coursework itself, you should master the following material.

1.Ch2-Boolean Algrebra-ICs-SUSTC.ppt and CH3-Minimisation-SUSTC in Sakai site.

2. Digital design lab6, Digital design lab7 and Digital design lab8 in Sakai site.
3. Verilog: http://www.verilog.com

EXERCISE SPECIFICATION

TASK1:

There are 4 wards, which are numbered from 1 to 4 respectively, among which the #1 ward has the lowest priority, and the #4 has the highest priority (Priority increases as the number increases). Each room has a call bell, it can be turn on and turn off. In the main control room there is a 7-seg tube which shows the ID of the room whose bell is on with the highest priority. Write a circuit to realize this function and test.

• Do the design.
• Write testbench to verify the function of your design.
• Create the constraint file.
• Do the synthetic and implementation, generate the bitstream file and program the device, then test on the Minisys/EGO1 develop board.

TASK2:

Implement a 4-16 decoder by two 3-8 decoders. You can either modify the provided

3-8 decoder in the or design 74138 decoder

• Do the design.
• Write testbench to verify the function of your design.
• Create the constraint file
• Do the synthetic and implementation, generate the bitstream file and program the device, then test on Minisys/EGO1 the develop board