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.

1 Solve each of the following 4-bit subtraction problems using 2’s complement representation.

1.            (00110)2 – (00101)2

2.            (0111)2 – (0001)2

Answer: The circuit has a Mode switch that allows you to choose between adding (M=0) and subtracting (M=1). To understand why this circuit works, let’s review binary addition and binary subtraction. We use 4-bit numbers in the examples because the main interactive circuit is a 4-bit adder–subtractor.

Binary addition is certainly easier than

2 What is difference between minterm and maxterm? Express the following function

F(x,y,z) = (x+z) y in form of minterm and maxterm?

Answer :Minterm and maxterm: Each row of a truth table can be associated with a minterm, which is a product (AND) of all variables in the function, in direct or complemented form. A minterm has the property that it is equal to 1 on exactly one row of the truth table.

3 Draw truth table for following Boolean function

1.            a) F(x,y) =(x+z)y

2.            b) F(x,y) = xy +xy’

Answer: Mathematics normally works with a two-valued logic: Every statement is either True or False. You can use truth tables to determine the truth or falsity of a complicated statement based on the truth or falsity of its simple components.

A statement in sentential logic is built from simple statements using the logical connectives ~ , v,^,-,. I'll construct tables which show how the truth or falsity of a statement built with these connective depends on the truth or falsity of its components.

4 Simplify the following Boolean function using k map.

F(A, B, C, D) = ∑m(0,2,3,5,6,7,8,10,11,14,15)

Answer:

3-variable Karnaugh maps:

Above we, place the 1's in the K-map for each of the product terms, identify a group of two, then write a p-term (product term) for the sole group as our simplified result.

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.

Sequential logic is used to construct

6. What is difference between Ring counter and Johson counter?

Answer : Ring counter

A ring counter is a type of counter composed of a circular shift register. If the output of a shift register is fed back to the input a ring counter results. There are two types of ring counters:

·         A straight ring counter or Over beck counter connects the output of the last shift register to the first shift register input and circulates a single one (or zero) bit around the ring. For example, in a 4-register one-hot counter, with initial

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