BCA1040 - DIGITAL LOGIC

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ASSIGNMENT

PROGRAM	BCA
SEMESTER	1
SUBJECT CODE & NAME	BCA1040/IMC1040- DIGITAL LOGIC
CREDIT	4
BK ID	B0948
MAX.MARKS	60

Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.

Q. 1 Convert each of the following hexadecimal numbers to binary, octal, and decimal formats.

I) (4FB2)16

ii) (DC4)16

Answer:- Hexadecimal numbers to binary:-

(4FB2)16 = (4*16³)+(F*16²)+(F*16¹)+(2*16⁰)

= (16384)+(15*256)+(15*16)+2

=16384+3840+240+2

Q.2 Construct the following gates using NAND

a) AND b) NOR c) XOR d)XNOR

Answer: - AND: - The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output (1) results only if both the inputs to the AND gate are HIGH (1). If neither or only one input to the AND gate is HIGH, a LOW output results. In another sense, the function of AND effectively

Q.3 Expand the following Boolean functions into their canonical form:

i. f(X,Y,Z)=XY+YZ+ X Z+ X Y

ii. f(X,Y,Z)=XY+ X Y + X YZ

Answer: - Canonical Forms:-Canonical forms express all binary variables in every product (AND) or sum (OR) term of the Boolean function. There are two types of canonical forms of a Boolean function. The first one is called sum-of product and the second one is called product-of-sum.

A’BC+A’BC’+ABC’+AB’C’+A’B’C’+ABC is a canonical sum-of-product form of a Boolean function, the given function has contained three inputs that

Q.4 Simplify the following Boolean function:

F = A’C + A’B + AB’C + BC, using K-map?

Answer:- A K-map shows the value of a function for every combination of input values just like a truth table, but a K-map spatially arranges the values so it is easy to find common terms that can be factored out. The image below shows the form of a 2,3 and 4 variable K-map.

Q.5 What are sequential circuits? Explain differences between sequential circuits and combinational circuits.

Answer:-Sequential circuits:-  In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present value of its input signals but on the past history of its inputs. This is in contrast to combinational logic, whose output is a function of only the present input. That is, sequential logic has state (memory) while combinational logic does not. Or, in other words, sequential logic is combinational logic with memory.

Q.6 What are shift registers? Explain serial in serial out shift register.

Answer: - A shift register is a cascade of flip flops, sharing the same clock, in which the output of each flip-flop is connected to the "data" input of the next flip-flop in the chain, resulting in a circuit that shifts by one position the "bit array" stored in it, shifting in the data present at its input and shifting out the last bit in the array, at each transition of the clock input. More generally, a shift register may be multidimensional, such that its "data in" and stage outputs are themselves bit arrays: this is implemented simply by running several shift

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