**UNIVERSITY EXAMINATIONS: 2010/2011 **

**FIRST YEAR STAGE EXAMINATION FOR THE DEGREE OF BACHELOR **

**OF SCIENCE IN INFORMATION TECHNOLOGY **

**BIT 1202: DIGITAL ELECTRONICS **

**DATE: AUGUST 2011 TIME: 2 HOURS **

**INSTRUCTIONS: Answer question ONE and any other TWO questions**

**Question One**

a) Write down the general expression for a number in base-r system. [1 Mark]

b) Do the following conversions:

i) (41.75)10 to binary [3 Marks]

ii) (513)10 to octal [3 Marks]

iii) (FFA)16 to decimal [3 Marks]

c) Find:

i) The 10’s complement of (754)10 and (378)10, [3 Marks]

ii) The difference (754-378) using 10’s complement [3 Marks]

iii) Evaluate the 2’s complement of (1010100)2 [3 Marks]

iv) Using 2’s complement find (1000011)2- (1010100)2. [3 Marks]

d) Represent (15)10 in :

i) Binary number [3 Marks]

ii) Binary code [3 Marks]

e) What is the binary result of the multiplication of unsigned binary numbers (10111010)2 and (111)2?

[3 Marks]

**Question Two**

a) Implement the function y = ab + ab −

using logic gates [4 Marks]

b) Write down the dual of the following Boolean expressions:

(i) x + y = y + x [4 Marks]

(ii) x( y + z) = xy + xz [4 Marks]

c) Find the complements of the following function:

i) A′BC′ + A′B′C [4 Marks]

ii) A(B′C + BC) [4 Marks]

**Question Three**

a) Define a flip-flop and explain how it works using a truth table. [6 Marks]

b) Distinguish between a combinational circuit and a sequential circuit. [4 Marks]

c) Describe the how a clock signal is incorporated in a D-Type Flip-flop. [5 Marks]

d) Using an illustration show how a four bit shift register can be implemented using D-Type Flip-flops

[5 Marks]

**Question Four**

a) Construct the Karnaugh map represented by the function F(x, y,z) = ∑(1,4,5,6). Write down the

algebraic expression for the POS, SOP and the minimized function. [10 Marks]

b) Draw the Karnaugh map for the Boolean function:

F(A, B,C, D) = ∑(0,1,8,9,10,11,13,15) With don’t care set d(A, B,C, D) = ∑(2,5,6,7,14) .

Write down the algebraic expression for the POS, SOP and the minimized function. [10 Marks]

**Question Five**

a) What is a multiplexer? [2 Marks]

b) Explain with the aid of a diagram how a two-input multiplexer works. [4 Marks]

c) Study the circuit below and construct a truth table. [10 Marks]

d) Explain the function of the circuit. [4 Marks]