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WSLiATE~ SRI LANKA INSTITUTE OF ADVANCED TECHNOLOGICAL EDUCATION(Establishedin the Ministryof HigherEducation,vide in Act No.29 of 1995)

Higher National Diploma in Information Technology

First Year, 1STSemester Examination -2013

IT 13 - Fundamentals of Digital System and Computer Hardware (Old)

Instructions for Candidates:

Answer five (05) questionsonly.

Time : Three (03) hours No of page : 04No of questions: 08

(1)

L) Convert each binary number to its equivalent decimal numbet.a. 1100011

b. 1011010.101

c. 110010.110

(06 marks)

ii.) Convert each decimal number to its equivalent binary number.a. 38

b. 123

c. 46.25

(06 marks)

iii.) Convert the following given numbers into relevant number format according to the

given table.

(08 marks)

(Total 20 Marks)

Binary Octal Hexadecimal

1010111

65D

367

11100111

(2)

(3)

i.) What is a signed binary number? (02 marks)

ii.) Determine the 1's complement of each binary number given below.a. 1011001

b. 1110101

c. 100100111

(06 marks)

iii.) Determine the 2's complement of each binary number given below.a. 11100100

b. 1101101

c. 1000111

iv.)

(06 marks)

Express the following decimal numbers as an 8 bit number in 1's complement form

and 2's complement form.a. -27

b. -17

(06 marks)

(Total 20 marks)

i.) Perform 2's complement subtraction of following numbers.

a) -1510+2510

b) 2010+ (-16)10(06 marks)

ii.) Multiply the following binary numbers.

a) 0011XOOll

b) 1001 x 0 III(06 marks)

iii.) Perform the following manipulations.

a) 9316+ DEI6

b) 458+238

(08 marks)

(Total 20 marks)

HNDIT -IT 13 Fundamentals of Digital System & Computer Hardware (Old) 2013

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(4)

i.)

ii. )

iii.)

(5)

Prove the following equations using the Boolean algebraic theorems.

a) XY + YZ + Y Z' = XY + Z

b) A + A' 13+ AB' = A + 13

(06 marks)

Simplify the following Boolean expressions. (' indicates the complement fonn'i.e. x)

a) (X + Y)(X + Z)

b) A'B+ AB'+ AB

c) ABC+AB'C+ABC' (09 marks)

Draw a logic diagram for the expression of C (A+ B) + A' (B + C') (05 marks)

(Total 20 marks)

i.) What is a universal gate? Give examples. (04 marks)

ii.) Find the Boolean expression for logic circuit shown in Fig.l below and reduce it

using Boolean algebra.

A

B

(06 marks)

v1.

Fig.J

iii.) A staircase light is controJled by two switches one at the top ofthe stairs and anotherat the bottom of stairs

a) Make a truth table for this system. (04 marks

b) Draw the circuit using AND-OR gates. (06 marks)

(Total 20 marks)

HNDIT -IT 13 Fundamentals'of Digital System & Computer Hardware (Old) 2013

~

(6)

i.) What is a k-map? (02 marks)

ii.) Reduce the following equation using k-mapY = A'B'C'+ AC'D'+ AB'+ ABCD'+ A'B'C (06 marks)

iii.) A combinational circuit has 3 inputs A, B. C and output F. F is true for following inputcombinations

A is False, B is True

A is False, C is True

A, B, C are False

A, B, C are True

a) Write the Truth table for F. Use the convention True=l and False = O.

b) Write the simplified expression for F in SOP form.

c) Write the simplified expression for Fin POS form.

d) Draw logic circuit using minimum number of 2-input NAND gates.

(04 marks)

(02 marks)

(02 marks)

(04 marks)

(Total 20 marks)

(7)

L) Distinguish between combinational logic circuits and sequential logic circuits. (04 marks)

ii.) What is a half-adder? (04 marks)

iii.) Explain a half-adder with the help of truth-table and logic diagram (12 marks)

(Total 20 marks)

(8)

i.) What is a Decoder? (04 marks)

ii.) Compare a decoder and a demultiplexer with suitable block diagrams. ". (08 marks)

iii.) Design a 32:1 multiplexer using two 16:1 multiplexers and a 2:1 multiplexer. (08 marks)

(Total 20 marks)

HNDIT -IT 13 Fundamentals of Digital Sy!,.tem& Computer Hardware (Old) 2013

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