How to Convert Decimal Numbers into Binary Numbers

By

 

How to Convert Decimal Numbers into Binary Numbers

The decimal to binary conversion involves dividing the decimal number by 2 repeatedly and recording the remainders. The binary number is obtained by reading the remainders from bottom to top.

Steps for Decimal to Binary Conversion

  1. Divide the decimal number by 2.
  2. Record the remainder (0 or 1).
  3. Divide the quotient by 2 again.
  4. Repeat until the quotient becomes 0.
  5. Read the remainders from bottom to top to get the binary equivalent.

Example 1: Convert 25₁₀ to Binary

Step-by-step Calculation

Division by 2QuotientRemainder
25 ÷ 2121
12 ÷ 260
6 ÷ 230
3 ÷ 211
1 ÷ 201

Final Answer: 25₁₀ = 11001₂

Example 2: Convert 43₁₀ to Binary

Division by 2QuotientRemainder
43 ÷ 2211
21 ÷ 2101
10 ÷ 250
5 ÷ 221
2 ÷ 210
1 ÷ 201

Final Answer: 43₁₀ = 101011₂

MCQs on Decimal to Binary Conversion

1. What is the binary equivalent of 10₁₀?

a) 1010₂

b) 1100₂

c) 1001₂

d) 1110₂

✅ Answer: a) 1010₂

2. What is the binary equivalent of 18₁₀?

a) 10010₂

b) 10100₂

c) 10011₂

d) 11000₂

✅ Answer: a) 10010₂

3. What is the binary equivalent of 50₁₀?

a) 110010₂

b) 101010₂

c) 100110₂

d) 111100₂

✅ Answer: a) 110010₂

4. The binary equivalent of 7₁₀ is:

a) 101₂

b) 110₂

c) 111₂

d) 100₂

✅ Answer: c) 111₂

5. Which of the following decimal numbers is represented as 1000₂ in binary?

a) 4₁₀

b) 6₁₀

c) 8₁₀

d) 10₁₀

✅ Answer: c) 8₁₀

Comments

Post a Comment

Popular posts from this blog

Shortcut Tricks for Average

By
  1. Quick Mental Math Techniques A. Choosing a Base Value for Faster Calculation Instead of summing all numbers directly, choose a base value close to the average and find deviations from it. Example:  Find the average of  48, 52, 46, 54, and 50 . Shortcut Trick:  Choose  50  as a base value because it is near most numbers. Now, calculate the deviations: 48 → -2 ,  52 → +2 ,  46 → -4 ,  54 → +4 ,  50 → 0 Total deviation =  (-2 + 2 - 4 + 4 + 0) = 0 New sum =  50 × 5 + 0 = 250 Average = 250 ÷ 5 = 50 ✅ Answer:  50  (calculated quickly without full addition). 2. Using the Difference Method for Faster Calculations This method is useful when numbers are close to a particular reference point. Example:  Find the average of  98, 102, 104, 96, and 100 . Shortcut Trick:  Choose  100  as the reference point. 98 → -2 ,  102 → +2 ,  104 → +4 ,  96 → -4 ,  100 → 0 Total deviation = ...
Read more

Types of Averages

By
  Types of Averages Averages are used to represent a central value of a dataset. The three main types of averages are: Arithmetic Mean (Mean) Median Mode 1. Arithmetic Mean (Mean) The  arithmetic mean  is the most common type of average, calculated by dividing the sum of all values by the number of values. Formula: Mean = Sum of all values Total number of values Mean = Total number of values Sum of all values ​ Example: Find the mean of  10, 20, and 30 . Solution: Mean = 10 + 20 + 30 3 = 60 3 = 20 Mean = 3 10 + 20 + 30 ​ = 3 60 ​ = 20 So, the  mean is 20 . 2. Median The  median  is the middle value when numbers are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers. Example 1 (Odd set of numbers): Find the median of  3, 5, 7, 9, 11 . Solution: Sorted order:  3, 5, 7, 9, 11 The middle number is  7 ,...
Read more

Problems on Averages

By
  1. Basic Problems: Finding the Average of Given Numbers The average (arithmetic mean) of a set of numbers is calculated using the formula: Average = Sum of all values Total number of values Average = Total number of values Sum of all values ​ Example: Find the average of  12, 18, 24, and 30 . Solution: Sum of numbers =  12 + 18 + 24 + 30 = 84 Total numbers =  4 Average = 84 4 = 21 Average = 4 84 ​ = 21 So, the  average is 21 . 2. Missing Number Problems: Finding the Missing Value When Average is Given When the average of a group is known, and one number is missing, we use the formula: Total Sum = Average × Total numbers Total Sum = Average × Total numbers Example: The average of  4 numbers  is  20 . Three of the numbers are  18, 22, and 19 . Find the missing number. Solution: Total sum =  Average × Total numbers Total Sum = 20 × 4 = 80 Total Sum =...
Read more