MGU UGP BCA ,S1 DIGITAL FUNDAMENTALS FIRST INTERNAL EXAMINATION , AUGUST 2025

 

ANSWER KEY

1.    Explain the non-positional number system with example?

A non-positional number system is a type of number system where the position of a digit does not affect its value. Each symbol or digit in the system has a fixed value, regardless of where it appears in the number.

EG: - ROMAN NUMBERS

2.    Explain the terms 1’s complement and 2’s complement?

The 1’s complement of a binary number is obtained by flipping all the bits:

Change every 1 to 0

Change every 0 to 1  Example:

Binary number: 0101 (which is 5 in decimal)
1’s complement: 1010

The 2’s complement of a binary number is obtained by:

Taking the 1’s complement of the number

Adding 1 to the result

🔹 Example:

Binary number: 0101 (5 in decimal)
1’s complement: 1010
Add 1: 1010 + 1 = 1011
2’s complement: 1011 (which represents –5)

3.    (a) Convert the hexadecimal number 5C2 to decimal?     

=(5×16^2)+(12×16^1)+(2×16^0) =(5×256)+(12×16)+(2×1)=

1280+192+2=1474

     (b) Convert the 10111101.011 to decimal?

     Decimal=189+0.375=189.375

4.    Explain the AND and OR gate with Truth table?

The AND gate outputs 1 only if both inputs are 1.

The OR gate outputs 1 if at least one input is 1.

5.    Explain briefly about 8421 codes. What are the rules for BCD addition. Explain with suitable example?

     The 8421 code is the Binary Coded Decimal (BCD) system, where:

     Each decimal digit (0–9) is represented by a 4-bit binary number.

The name 8421 comes from the weights of each binary digit:
8, 4, 2, and 1

When adding two BCD numbers:

Add the BCD digits as regular 4-bit binary numbers.

If the sum is ≤ 9 (1001) and there is no carry, the result is valid BCD.

If the sum is > 9 or a carry is generated, add 6 (0110) to correct the result and produce valid BCD.

6.    (a) Write a short note on the binary addition and subtraction.

Add 10111+01101

Sub 1101-0110

 

Add each bit from right to left, remembering that:

0 + 0 = 0

1 + 0 = 1

1 + 1 = 10 (which is 0 with a carry of 1)

1 + 1 + 1 = 11 (which is 1 with a carry of 1

Addition result -      100100

Subtraction result -  0111

7.    Explain decimal to octal conversion. Convert decimal number 163 to octal?

The octal number system is a base-8 number system. It uses digits from 0 to 7.
To convert a decimal (base-10) number to octal (base-8), we use the repeated division method.

Steps to Convert Decimal to Octal:

Divide the decimal number by 8.

Write down the remainder.

Divide the quotient again by 8.

Repeat until the quotient becomes 0.

The octal number is the remainders read in reverse order (from last to first).

163 ÷ 8

20

3

20 ÷ 8

2

4

2 ÷ 8

0

2

            Now, write the remainders in reverse order:   2 4 3

8.    Write a short note on number system and its uses with example?

A number system is a way of representing numbers using a set of symbols or digits. It defines how numbers are expressed and calculated in mathematics and digital systems.There are different types of number systems based on their base (or radix) — which is the total number of digits used.

 

 

🔹 Types of Number Systems and Their Uses:

Number System

Base

Digits Used

Common Uses

Decimal

10

0–9

Used in everyday counting and arithmetic

Binary

2

0, 1

Used in computers and digital electronics

Octal

8

0–7

Used in early computing and compact binary representation

Hexadecimal

16

0–9, A–F

Used in computer memory addressing and programming

 

 9. (a) State and explain the 3 different methods of converting decimal to binary?     

     (b) Convert 45.3125 to binary show up to 4 decimal places? 

a)  Division Method (for Integer Part)

This method is used for converting whole numbers.

Sum of weights method

Repeated multiplication by 2

b)  45 ÷ 2 = 22 remainder 1 

22 ÷ 2 = 11 remainder 0 

11 ÷ 2 = 5  remainder 1 

5 ÷ 2  = 2  remainder 1 

2 ÷ 2  = 1  remainder 0 

1 ÷ 2  = 0  remainder 1

45.3125 (decimal) = 101101.0101 (binary)

 10. Explain the different logic gates with truth table and graphical representation?

Logic gates are the basic building blocks of digital circuits. They perform logical operations on one or more binary inputs to produce a single binary output.

AND,OR,NOT,XOR,XNOR,NAND,NOR

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