Anna University

CS2202 / 141302 Digital Principles and Systems Design IMPORTANT 16marks

(DPSD)

Subject Code : CS2202

Subject Name :Digital Principles and Systems Design

Department :CSE and IT

Semester :3

16 Marks

UNIT I

1 (i). Express the Boolean function F =A+B’C in sum of minterms

(ii) Express the Boolean function F=xy+x’z in production of maxterms.

Solution:

F = A+B’C

= A’B’C’+AB’C+AB’C+ABC’+ABC

= m1 + m4 + m5 + m6 + m 7

=_m (1,4,5,6,7)

F = XY+X’Z

= (X+Y+Z)(X+Y’+Z)(X’+Y+Z)(X’+Y+Z’)

= M 0 M 2 M 4 M 5

= P (0,2,4,5)

2.Simplify the Boolean function F(A,B,C,D)= _(0,6,8,13,14) Together with the don’t

care condition d=_(2,4,10)and then express the simplified function in sum of

minterms.

¨ Using 4-variable map simplify the function as

F=B’D’+CD’+ABC’D

¨Represent the simplified function in SOP from as

F=_(0,2,6,8,10,13,14)

3.Implement the Boolean function F(X,Y,Z)=(1,2,3,4,5,7)with NAND gates

¨Simplify the function using 3-varabile map and express it SOP from as

F=XY’+X’Y+Z

¨Draw a NAND gate for each product term of the expression. This gives a

group of first level gates.

¨Draw a single gate using the AND –invert or the invert -OR graphic simple

in the second level, with inputs coming from outputs of first level gates.

4. Simplify the Boolean function F(A,B,C,D) =_(0,2,3,5,7,8,9,10,11,13,15)and find the

prime implicants and essential prime implicants

¨ Simplify the expression using 4-varible map,

¨ Prime implicants are :CD,B’C,AD AND AB’

¨ Essential prime implicants are :CD,B’C,AD AND AB’

¨ Different simplified versions are :BD and B’D’

F=BD+B’D+CD+AD

F=BD+B’D+CD+AB’

F=BD+B’D+B;C+AD

F=BD+B’D’+B;C+AB’

5.Minimize the following function sing Quine Mc Cluskey Method

• List all minterms in the binary form

• Arrange minterms according to categories of 1 in a table

• Compare each binary number with every term in the next higher category and if

they differ only one position put a check mark and copy the term in the next

column with a – in the position that they differed.

• Continue the process until no further elimination of literals

• List the prime implicants

• Select the minimum number of prime implicants

UNIT II

1.Design a full adder with inputs x,y,z and two outputs S and C . The circuit performs

x+y+z, z is the input carry, C is the output carry and S is the Sum.

• Truth table for full adder

• Simplify using K map

• Draw the logic diagram using AND and XOR gate

• Draw the logic diagram using 2 half adders

2. Design a BCD adder.

• Explanation on BCD addition

o Add 2 BCD numbers using ordinary binary addition

o If sum >=9 no correction is needed

o If sum >=9 or if a carry is generated the sum is invalid

o To correct the invalid sum add 0110 to the sum. If a carry results from this

addition add it to the next higher order BCD digits.

• Draw the truth table with 4 inputs

• Simplify output using 4 variable map

• Draw the logic diagram

3. Design a logic circuit that accepts a 4-bit Grey code and converts it into 4-bit

binary code

• Draw the truth table with 4 inputs G3,G2,G1andG0 and 4 0utputs D,C,B and

A.

• Simplify the columns A,B,C and D using 4-variables map

A=(G3 XOR G2)XOR(G1 XOR G0)

B=G3 XOR G2 XOR G1

C=G3 XOR G2

D=G3

• Draw the logic diagram using xor gates with G3,G2,G1 and G0 as Input and

A,B,C and D as output

4.Write short notes on: BCD adder, Binary multiplier and Magnitude Comparator

o BCD adder truth table

o Block diagram of BCD adder

o Logic diagram for 2-bit by 2-bit binary multiplier

o 4-bit magnitude comparator

5.Explain in detail the Hardware Description Languages

• Module representation

• Gate delays

• Boolean expressions

• User -defined primitives

• Explanation of the above with suitable examples

UNIT-III

1.Draw the circuit for 3-to-8-decoder and implement the functions

F1(A,B,C)=II(0,1,3,7)

F2(A,B,C)=II(2,3,7) using 3-to-8-decoder

• Truth table for a 3-to-8-decoder(i/p: E,A,B,C and o/p:Y7-Y0)

• Logic diagram

• Block diagram of 3:8 decoder using IC74LS183 WITH A,B,C as input and

F1,F2 as output

2.Draw the circuits for Decimal to BCD encoder, Octal-to-Binary encoder & Priority

encoder

• Decimal to BCD encoder-logic symbol(74LS147,truth table)

• Octal to binary encoder truth table with inputs D0 - D7 and outputs A , B

and C

• Logic diagram of Octal to binary encoder: A=D4+D5+D6+D7;

B=D2+D3+D6+D7; C=D1+D3+D5+D7

• Priority encoder - truth table with i/ps : D0,D1,D2,D3 and o/ps: Y1,Y0,V

• Logic diagram of Priority encoder where Y1=D2+D3,Y0=D3+D1D2',

V=D1+D2+D3

3.Implement the following boolean function using 8:1 multiplier

• F(A,B,C,D)=A'BD'+ACD+B'CD+A'B'CD+A'BC'D+A'B'C'D

• Draw the Truth table for the above SOP(I/P's:A,B,C,D, o/p: Y)

• Draw the implementation table 8:1 multiplexer, where

D0=0,D2=0,D1=D3=1,D4=D5=D6=A',D7=A

4.Implement full subtractor using demultiplexer

• Truth table of full subtractor(i/p:A,B,Bin,o/pL,Bout)

• D=F(A,B,C)= m(1,2,4,7)

• Bout=F(A,B,C)= m(1,2,3,7)

• Draw 1:8 demultiplexer with the input Din=1 and output D and Bout.

5.Implement the following Boolean function with a PLA

F1(A,B,C)= m(0,1,2,4)

F2(A,B,C)= m(0,5,6,7)

• Simplify F1 and F2 using k-map

F1(A,B,C)=(AB+AC+BC)'

F2(A,B,C)=AB+AC+A'B'C'

• Draw the PLA programming table with minterms

AB,AC,BC&A'B'C'

UNIT IV

1. Draw the state diagram and characteristic equations of T,D and JK flip flop

• Characteristic equation of T flip flop: Q(t+1)=TQ'+T'Q

• Characteristic equation of D flip flop: Q(t+1)=D

• Characteristic equation of JK flip flop: Q(t+1)=JQ'+K'Q

• state diagrams of T,D and JK flip flops

2. Write short notes on state reduction and state assignment in Sequential circuit

design

State reduction

• Given a state diagram of a sequential circuit. Establish the

corresponding state table

• Find the equivalent states that produce the same output for every

input and the same next state

• Draw the reduced state table by removing one of the equivalent

state

• Draw the corresponding reduced state diagram

State assignment

• Binary assignment

• Gray code assignment

• One-hot assignment

3. Discuss in detail shift registers

• Block diagram of 4-bit shift register

• Serial transfer of information

• serial addition using shift register

• Universal shift register

4.Discuss about synchronous counters

• binary counter:4-bit synchronous binary counter, with parallel load

• Up-down counter

• BCD counter

5.Write the procedure for analyzing a clocked sequential circuit with JK flip flop

• Given a logic diagram. From this ,write the state equations

• Establish the state table

• Draw the state diagram

• Write the flip flop input equations and the output equation, if any.

UNIT -V

1.Explain the procedure for analyzing an asynchronous sequential circuit with SR

latches with example

• Given an asynchronous sequential circuit with SR latch

• Label each latch output with Yi and its external feedback path with Yi

• Derive the Boolean functions for the Si & Ri input in each latch

• check whether SR=0 for each NOR latch or whether S'R' =0 for each

NAND latch

• Evaluate Y=S+R'y for each NOR latch or Y=S'+Ry for each NAND latch

• Construct a map with the y's representing the rows and the x inputs

representing the columns

• Plot the value of Y=Y1Y2.......in the map

• Circle all stable states where Y=y. The resulting map is then the transition

table.

2.Explain the procedure for designing an asynchronous sequential circuit with an

example obtain a primitive flowtable from the given design specifications

• Reduce the flow table by merging rows in the primitive flowtable

• Assign binary values to the state variables to obtain the transition tables

Assign output values to unstable states to obtain the output maps

• Simplify the Boolean functions of the excitations and output variables and

draw the logic diagram.

3.Discuss in detail the procedure for reducing the flowtable with an example

• Determine all the compatible pairs by using implication table

• Find the maximal compatibles using the merger diagram

• Find the minimal collection of compatibles that covers all the states and is

closed

• The minimal collection is used to merge the rows of the flow table

4.write short notes on race-free state assignment

• Three row flowtable example

• Four row flowtable example

• shared row method

• Multiple row method

5.Explain in detail Hazards

• Hazards in combinational circuits

_ Explanation with example

_ (Static 1-Hazard,Static 0-Hazard&Dynamic Hazard)

• Hazards in sequential circuit

_ Implementation with SR latches

_ Essential Hazards.

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