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1. Dear students get fully solved assignments
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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 Add the following 8-bit binary numbers
i. (01001110)2 + (00111100)2
ii. (10011101)2 + (10001111)2
Answer : Binary Arithmetic:-The arithmetic operations - addition, subtraction, multiplication and
division, performed on the binary numbers is called binary arithmetic . In computer systems, the
basic arithmetic operations performed on the binary numbers is -
 Binary Addition, and
 Binary Subtraction,
In the following subsections, we discuss the binary addition and the binary subtraction operations.
Binary addition involves adding of two or more binary numbers. The binary addition rules are used
while performing the binary addition. Table 1 shows the binary addition rules.
Binary Addition:-Binary addition involves adding of two or more binary numbers. The binary
addition rules are used while performing the
2 Explain the rules for simplifying functions using Karnaugh maps.
Answer : The Karnaugh map uses the following rules for the simplification of expressions
by grouping together adjacent cells containing ones

2.  Groups may not include any cell containing a zero
 Groups may be horizontal or vertical, but not diagonal.
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-
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,
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 finite state

3. 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
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