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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