**UNIVERSITY EXAMINATIONS: 2012/2013**

**FIRST YEAR EXAMINATION FOR THE BACHELOR OF SCIENCE **

**IN INFORMATION TECHNOLOGY**

**BIT 1202 DIGITAL ELECTRONICS**

**DATE: DECEMBER, 2012 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question ONE and any other TWO**

**QUESTION ONE**

a) Perform the following conversions;

i) 693.56 (decimal) to Octal, corrected to 4 fractional places of Octal.

ii) 437.6 (octal) to Hexadecimal (6 Marks)

b) Copy and fill the Multiplication table for the Octal (base–8) given by the formula,

P(8) = A(8) x B (8) show your working how you have obtained P1 to P8.

(4 Marks)

c) Given that only NOR- gates are readily available, show how you would replace

the following logic gates with 2–input NOR-gates only; (include symbols, logic

expressions and equivalent circuits)

i) A 2–input AND–gate

ii) A 2–input OR–gate. (4 Marks)

d) i) Convert the Gray–code 1 1 0 0 1 0 1 1 1 0 1 to its equivalent Binary

word. Explain the steps.

ii) Convert the Binary word 1 1 0 0 1 0 1 1 1 0 1 to its equivalent Gray–

code. Explain the steps. (4 Marks)

e) Reduce (Simplify) the logic expression using the laws of Boolean algebra and

express each as an SOP.

i)

ii) (6 Marks)

f) Draw and label the logic symbol and truth table for each of the following 2-input

logic gates:

i) NAND ii) OR iii) Exclusive-OR (XOR) (6 Marks)

**QUESTION TWO**

a) A digital logic system has a function represented by the circuit in Fig. Q2

i) Copy the figure and label the output of each of the gates

ii) Derive the raw form of the expression for the output function F

iii) Hence simplify (reduce) the logic expression of F as a simplified Sum-ofProducts (SOP). (6 Marks)

b) A function X is given by the expression

i. Draw the logic circuit diagram of X using basic logic gates only.

ii. Draw the truth–table for the function X.

iii. Write down the standard SOP expression of X in terms of its

minterms and equivalent decimal numbers. (8 Marks)

c) i) A logic function is given by . Draw the logic circuit

using 2-input NOR –gates only.

ii) An SOP logic function is expressed as . Draw the logic

circuit of the function Z using 2–input NAND–gates only. (6 Marks)

**QUESTION THREE**

a) Tabulate a 3–bit Binary code ( in ascending order ) and its equivalent 3–bit Gray

code. (8 Marks)

b) A logic function is expressed as F(A, B,C) give a HIGH output (F=1) when the

equivalent decimal numbers are 0, 2, 3, 4, 5

i) Derive the standard SOP expression of the function F.

ii) Draw the K-map for function F.

iii) Use the K-map and derive the simplified SOP expression of the function

F.

iv) Hence or otherwise derive the simplified POS expression of the same

function

(12 Marks)

**QUESTION FOUR**

a) Copy and fill in appropriately the coding systems given in the table below

(16 Marks)

b) Represent the decimal number 639, using equivalent binary in;

i) BCD code

ii) Excess–3 code (4 Marks)

**QUESTION FIVE**

a) Name what are referred to as universal gates and state any two advantages these gates

have over the basic gates. (4 Marks)

c) Using the filled table in part (b) write down the function F in terms of

i) Standard Sum-of–Products (SOPs)

ii) Standard Product- of–Sums(POSs)

iii) The equivalent digits of the minterms

iv) The equivalent digits of the maxterms (8 Marks)