1. PROJECT ON-
DIGITAL LOGIC AND
DESIGNING
NAME-ASTHA CHAURASIA
BRANCH-AIML 0901AM221023
SUMBITTED TO –Dr.SAUMIL MAHESHWARI
2. WHAT IS NUMBER SYSTEM
A number system is a system representing numbers. It is also called the system
of numeration and it defines a set of values to represent a quantity.
Types of Number Systems
Binary number system
(Base - 2) like that (110101)2
Octal number system
(Base - 8) like that (826)8
Hexadecimal number system
(Base - 16) like that (27FBE)16
Decimal number system
(Base - 10) like that (102345)10
3. CONVERSION EXAMPLE
Let us Convert the Decimal Number 75 into a Binary Number.
Division of
Decimal
Number by 2
Quotient Remainder Binary
75/2 37 1 (LSB) 1
37/2 18 1 1
18/2 9 0 0
9/2 4 1 1
4/2 2 0 0
2/2 1 0 0
1/2 0 1 (LSB) 1
4. DEFINITION OF ADDER
• An adder is a digital logic circuit in electronics that
implements addition of numbers.
Half Adder
The half adder accepts two binary digits on its inputs and produce two binary digits outputs
a sum bit and a carry bit
INPUTS OUTPUTS
A B SUM CARRY
0 0 0 0
o 1 1 0
1 0 1 0
1 1 0 1
SUM=A’B+AB’
=A ⊕B
CARRY =AB
5. FULL ADDER
• The full adder accepts three binary digits on its inputs and produce two
• binary digits outputs a sum bit and a carry bit.
• SUM = A′B′C + A′BC′+ AB′C′+ ABC
• = A′(B′C+BC′) + A (B′C′+BC)
• = A′(B ⊕ C) + A(B ⊕ C)′
• =A’P +AP’ let B ⊕ C=P
• =A ⊕p
• = A ⊕ B ⊕ C
• CARRY=A’BC+AB’C+ABC’+ABC
• =C(A’B+AB’)+AB(C’+C)
• =C(A ⊕B)+AB
INPUT OUTPUT
A B C SUM CAR
R
Y
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
