HOMEWORKS

HomeWork-01 (Score/10 = 10 points) ----- Deadline - Jan 11,2015

What is the first known computing Device ? (2) Which Generation does it belong ? (2)

Who created the Slide Rule.(1) What Mathematical functions (Give 10) can you perform using a Slide Rule. (5)

What are the Generation of Computers and their Time Period.(5) Give example for each.(5)

What is the First Programming Language employed in computers. (2)

Name 10 other Programming Languages for computers.(5)

Draw a Computer Block Diagram using the Von Neuman Model. (5)

What are the 5 main components of a Computer in a Von Neuman Model. (5)

Name 5 types of Hardware being employed in a computer today. (5)

Name at least 30 people who contributed to the development and progress of Computers and give their contribution. (30)

Name 10 differences between ANALOG and DIGITAL computing devices. (10)

Give 3 examples of USES or APPLICATIONS or CIRCUITS for ANALOG DEVICES (3) and for DIGITAL DEVICES. (3)

Give 3 components used in ANALOG DEVICES (3) and in DIGITAL DEVICES. (3)

Name 7 Basic Logic Gates used in Digital Devices. (7)

HomeWork-02 (Score/8 = 10 points) ----- Deadline - Jan 18,2015

1-3.*Convert the following binary numbers to their equivalent decimal values.(3)

(a) 11001

(b) 1001.1001

(c) 10011011001.10110

1-7.*What is the maximum number that we can count up to using 10 bits? (1)

1-8. What is the maximum number that we can count up to using 14 bits? (1)

1-9.*How many bits are needed to count up to a maximum of 511? (1)

1-10. How many bits are needed to count up to a maximum of 63? (1)

1-13.*Suppose that the decimal integer values from 0 to 15 are to be transmitted in binary.(2)

(a) How many lines will be needed if parallel representation is used?

(b) How many will be needed if serial representation is used?

1-14. How is a microprocessor different from a microcomputer? (2)

1-15. How is a microcontroller different from a microcomputer? (2)

2-1. Convert these binary numbers to decimal. (3)

(a) 10110

(b) 10010101

(c) 100100001001

2-2. Convert the following decimal values to binary. (3)

(a) 37

(b) 13

(c) 189

2-3. What is the largest decimal value that can be represented by

(a) an 8-bit binary number? (1)

(b) A 16-bit number? (1)

2-4. Convert each hex number to its decimal equivalent. (3)

(a) 743

(b) 36

(c) 37FD

2-5. Convert each of the following decimal numbers to hex.(3)

(a) 59

(b) 372

(c) 919

2-6. Convert each of the hex values to binary.(8)

(a) 743 (d) 2000 (g)*7FF

(b) 36 (e)*165 (h) 1204

(c) 37FD (f) ABCD

2-7. Convert the binary numbers to hex.(8)

(a) 10110 (d) 01101011 (g) 1111010111

(b) 10010101 (e) 11111111 (h) 11011111

(c) 100100001001 (f) 01101111

2-9. When a large decimal number is to be converted to binary, it is sometimes easier to convert it first to hex, and then from hex to binary.

Try this procedure for Decimal value 2133. (2)

2-10. How many hex digits are required to represent decimal numbers up to 20,000? (1)

2-19. Encode these decimal numbers in BCD. (8)

(a) 47 (d) 6727 (g) 89,627

(b) 962 (e) 13 (h) 1024

(c) 187 (f) 529

2-20. How many bits are required to represent the decimal numbers in the range from 0 to 999 using (a) straight binary code? (b) Using BCD code? (2)

2-21. The following numbers are in BCD. Convert them to decimal.(6)

(a) 1001011101010010 (d) 0111011101110101

(b) 000110000100 (e) 010010010010

(c) 011010010101 (f) 010101010101

2-22. (a) How many bits are contained in eight bytes?

(b) What is the largest hex number that can be represented in four bytes? (2)

(c) What is the largest BCD-encoded decimal value that can be represented in three bytes? (2)

2-23. (a) Refer to an ASCII Table. What is the most significant nibble of the ASCII code for the letter X? (2)

(b) How many nibbles can be stored in a 16-bit word? (2)

(c) How many bytes does it take to make up a 24-bit word? (2)

2-24. Represent the statement “X = 3*Y ” in ASCII code. Attach an odd parity bit. Show answer in HEX and Binary. (5)

2-26. The following bytes (shown in hex) represent a person’s name as it would be stored in a computer’s memory. Each byte is a padded ASCII code.

Determine the name of each person.

(a) 42 45 4E 20 53 4D 49 54 48 (2)

(b) 4A 6F 65 20 47 72 65 65 6E (2)

2-27. Convert the following decimal numbers to BCD code and then attach an odd parity bit. (6)

(a) 74 (c) 8884 (e) 165

(b) 38 (d) 275 (f) 9201

HomeWork - 003

I- Show the output signals for the following GATES with their corresponding INPUTS.

Show also the TRUTH Table for this GATE.

1)

2)

3)

4)

5)

6)

7)

8) DRAW the LOGIC Circuit that will produce the output X for the corresponding

inputs A and B shown below.

9) DRAW the LOGIC Circuit that will produce the output X for the corresponding

inputs A and B shown below.

10) Get the simplified Boolean function F. Then using the techniques of Bubble Pushing and

the Universality of NAND Gate, find the equivalent Logic Circuit using only minimal number

of NAND Gates. (use De Morgans Theorem)

HomeWork - 004

I - Simplify the Boolean Functions Below using Boolean Theorems.

1) f = x' + y' + (x y)' + (x y)' z

2) F = XY + XZ' + XZ

3) F = A(BC)' + AB + (AC)'

4) f = x + x'y + x + y'

5) F = B(A + B) + AB' + B'

6) f = (x + y + z)(x'y + y'z)

7) f = xy + xyz' + x'y'

8) F = A'BC + ABC + BC'

9)

10)

II - SImplify the Boolean Functions and then DRAW the LOGIC circuit to implement the simplified form.

1) f = [ (a + b')(a' + b) ]'

2) f = [ ( A' + B' )( E' + F') ]'

3) f = ( X + X'Z) (X + Z)

4) X = ( A' + B' + C') + (ABC)'

5) Using the above function, solve for Z = X' , where Z is the complement of Function X.

HomeWork-05

(Score = 0.5/K-Map Total = 15) Deadline - March 9,2015

Get the Boolean Expression for the following K-Maps.

EXERCISES - Logic Circuits Design

For all your Design Solutions, Show the Truth Table, Boolean Expression in SOP and the Implementation using 2-Level Gates.

DESIGN 1

DESIGN 2

HINTS ( Operation is Different from Design #1)

Initial Conditions:

A=1, B=0, C=0 and F=0 (Lights OFF)

Changing the position of any switch causes the light to come on

Changing the position of any switch again causes the light to go off

DESIGN - 4

Design a 4-bit prime number detector (or, Given a 4-bit input

combination N3N2N N0, design a Logic Circuit that produces a

Function F(N3 N2 N1 N0) = 1 for all Prime Numbers and a “0”

output for all other numbers)

f (N3,N2,N1,N0) = (1,2,3,5,7,11,13)

For Design-5 Implement only the Logic CIrcuit for the output GT where

AB > CD. YOu need to complete the Truth Table.

Assignment 006

1) Q- Obtain a 4 to 16 decoder using (a) 2 to 4 decoder (b) 3 to 8 decoder.

2) Q- Obtain a 3 to 8 decoder using (a) 2 to 4 decoder,

3) Q- Implement the Full adder using 3 to 8 decoder.

EXERCISES - Analysis of Sequential Circuits

You can try some of these exercises which covers the analysis and design of sequential circuits.

Analysis of Sequential Circuits.

1. Derive a) excitation equations, b) next state equations, c) a state/output table, and d) a state diagram for the circuit shown in Figure 1.1. Draw the timing diagram of the circuit.

Figure 1.1

2. Derive a) excitation equations, b) next state equations, c) a state/output table, and d) a state diagram for the circuit shown in Figure 1.2.

Figure 1.2

3. Derive a) excitation equations, b) next state equations, c) a state/output table, and d) a state diagram for the circuit shown in Figure 1.3.

Figure 1.3

4. Derive the state output and state diagran for the sequential circuit shown in Figure 1.4.

Figure 1.4

5. A sequential circuit uses two D flip-flops as memory elements. The behaviour of the circuit is described by the following equations:

D1 = Q1 + x'*Q2

D2 = x*Q1' + x'*Q2

Z = x'*Q1*Q2 + x*Q1'*Q2'

Derive the state table and draw the state diagram of the circuit.

Design of Sequential Circuits.

6. Design a sequential circuit specified by Table 6.1, using JK flip-flops.

Table 6.1

Present State

Next State

Output

Q0 Q1

x = 0

x = 1

x = 0

x = 1

7. Design the sequential circuit in question 6, using T flip-flops.

8. Design a mod-5 counter which has the following binary sequence: 0, 1, 2, 3, 4. Use JK flip-flops.

9. Design a counter that has the following repeated binary sequence: 0, 1, 2, 3, 4, 5, 6, 7. Use RS flip-flops.

10. Design a counter with the following binary sequence: 1, 2, 5, 7 and repeat. Use JK flip-flops.

11. Design a counter with the following repeated binary sequence: 0, 4, 2, 1, 6. Use T flip-flops.

12. Design a counter that counts in the sequence 0, 1, 3, 6, 10, 15, using four a) D, b) SR, c) JK and d) T flip-flops.

Quiz

To refresh on what you have learnt so far.

1. A sequential circuit is a digital circuit whose logic states depend on a specified time sequence.

True False

2. Sequential circuits contain only combinational logics.

True False

3. Sequential circuits contain memory and combinational circuits do not.

True False

4. The outputs of a sequential circuit are computed using both the present and past input values.

True False

1. Sequential circuits can be synchronous and asynchronous.

True False

2. A synchronous sequential circuit changes its states at discrete instants of time.

True False

3. Asynchronous sequential circuits can have state transitions at discrete instants of time.

True False

4. Synchronous sequential circuits are also known as clocked sequential circuits.

True False

5. A transition of a clock from 0 to 1 is called the falling edge.

True False

6. The clock period is the time when the clock signal is equal to 1.

True False

7. The memory used in synchronous sequential circuits are flip-flops.

True False

1. A JK flip-flop is presently in the RESET state and must go to the SET state on the next clock pulse. J must be 1 and K must be X (don't care).

True False

2. A JK flip-flop is presently in the SET state and must remain SET on the next clock pulse. Then J must be X and K must be 1.

True False

3. A RS flip-flop is presently in a SET state and must go to the RESET state on the next clock pulse. S must be 1 and R must be 0.

True False

4. For a D flip-flop, the next state is always equal to the D input.

True False

5. For a D flip-flop, when the present state Q=0 goes to the next state Q=1, the required D input is D=1

True False

1. State table and state diagram represents exactly the same information.

True False

Table 1. State table

Present State

Next State

Output

Q0 Q1

x = 0

x = 1

x = 0

x = 1

2. Consider the state table in Table 1. If the circuit is in the present state 01, for input x=0, the next state would be 11 and the output is equal to 1.

3. Consider the state table in Table 1. Initially, present state is 00. For an input x=1, the next state of the circuit is 01. After the next clock pulse, the present state would become 10.

True False

Figure 1.

State diagram

4. For the state diagram in Figure 1. When the circuit is in state 00, the label 1/0 means that the circuit will go to the next state 10.

5. For the same state diagram in Figure 1. If the present state is 01, and the input is 0, the next state would be 10.

6. For the same state diagram in Figure 1. If the circuit is presently in state 11, it will remain in its present state 11 if the input is 0 and the output is 0.

7) DO a STATE REDUCTION for the State Diagram Below.

8)

Č

đ

Add files