Question 1

?Why is understanding binary to decimal conversion important in computer science and digital electronics

Accepted Answer

Understanding binary to decimal conversion is crucial in computer science and digital electronics because computers and digital systems use binary (base-2) numbering as their fundamental language. Binary numbers represent all types of data, including instructions and information processing. Converting binary to decimal (base-10), which is the numbering system humans commonly use, allows us to interpret and manage data more effectively. This conversion process is essential for debugging, programming, understanding machine-level instructions, and interfacing digital systems with human operators and other non-binary systems.

Write down the binary number and assign powers of 2 to each digit, starting from the right (least significant bit) to the left (most significant bit).

1
×
2
5
=
32
0
×
2
4
=
0
1
×
2
3
=
8
1
×
2
2
=
4
0
×
2
1
=
0
1
×
2
0
=
1
1
0
1
1
0
1
​
  
×2 
5
 =32
×2 
4
 =0
×2 
3
 =8
×2 
2
 =4
×2 
1
 =0
×2 
0
 =1
​
 
Add all the results together:

32
+
0
+
8
+
4
+
0
+
1
=
45
32+0+8+4+0+1=45
So, the decimal equivalent of the binary number 101101 is 45.

Question 2

?How would you convert the binary number 1110101 to its decimal equivalent step-by-step

Accepted Answer

To convert the binary number 1110101 to its decimal equivalent, follow these steps:

Write down the binary number and assign powers of 2 to each digit, starting from the right (least significant bit) to the left (most significant bit).

1
×
2
6
=
64
1
×
2
5
=
32
1
×
2
4
=
16
0
×
2
3
=
0
1
×
2
2
=
4
0
×
2
1
=
0
1
×
2
0
=
1
1
1
1
0
1
0
1
​
  
×2 
6
 =64
×2 
5
 =32
×2 
4
 =16
×2 
3
 =0
×2 
2
 =4
×2 
1
 =0
×2 
0
 =1
​
 
Add all the results together:

64
+
32
+
16
+
0
+
4
+
0
+
1
=
117
64+32+16+0+4+0+1=117
So, the decimal equivalent of the binary number 1110101 is 117.

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Binary to decimal conversion fundamentals for beginners

Mathematics

How to Get The Certificate

Number Systems Decimal Number System STLD Lec 01

9 s Complement 10 s Complements Decimal Number STLD Lec 02

Decimal to Binary number system STLD Lec 03

Binary to decimal Conversions Decimal to Binary Decimal Point STLD Lec 04

Binary addition and Subtraction Multiplication and Division STLD Lec 05

Signed numbers 2 s Compliment Representation STLD Lec 06

1 s and 2 s complement Solved Examples STLD Lec 07

Binary to Octal conversion Octal to Binary Decimal Point STLD Lec 08

Decimal to Octal conversion Octal to Decimal Decimal Point STLD Lec 09

Binary to Hexadecimal Conversion Hexadecimal to Binary Decimal Point STLD Lec 10

Decimal to Hexadecimal conversion Hexadecimal to Decimal Decimal Point STLD Lec 11

Octal to hexadecimal Conversion Decimal Point Vice Versa STLD Lec 12

Hexadecimal arithmetic Addition Substration STLD Lec 13

Codes Classification Cyclic reflective codes STLD Lec 14

BCD Addition Subtraction STLD Lec 15

BCD subtraction 9 s and 10 s complement STLD Lec 16

Excess 3 code Table addition Substation STLD Lec 17

Excess 3 Code Subtraction 9 s and 10 s complement STLD Lec 18

Gray code Binary to Gray conversion STLD Lec 19

Logic gates AND OR NOT STLD Lec 20

NAND gate 2 i p Universal gate STLD Lec 21

NOR gate 2 i p Universal gate STLD Lec 22

Exclusive OR gate Truth Table Properties STLD Lec 23

Exclusive NOR gate Truth Table STLD Lec 24

Inhibit circuits Enable STLD Lec 25

Boolean Expression Examples Solved STLD Lec 26

Logic gates Pulsed operation STLD Lec 27

Boolean algebra Axioms and laws Part 1 2 STLD Lec 28

Boolean algebra Axioms and laws Part 2 2 STLD Lec 29

Boolean expressions Simplification STLD Lec 30

Boolean functions Representation SOP POS STLD Lec 31

Canonical forms Minterms Maxterms Conversion STLD Lec 32

Basic gates to NAND NOR gate Conversion STLD Lec 33

AOI to NAND Conversion NOR Examples STLD Lec 34

What is K map Introduction Two variable STLD Lec 35

K Map 3 variable SOP Example STLD Lec 36

K map 3 Variable POS Minimization STLD Lec 37

Full adder circuit using k map 3 variable STLD Lec 38

K Map 4 variable SOP Example STLD Lec 39

k map 4 variable POS STLD Lec 40

Real numbers

Statistics

Quadratic Equation

Polynomials

Pair of Linear Equations in Two Variables

Coordinate Geometry

Arithmetic Progression

Areas Related to Circles

Circles

Application of Trigonometry

Triangles

Surface Area and Volumes

Youth Empowerment

Algebra

Algebra

Discrete Mathematics