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2 <p>Last updated on<strong>September 30, 2025</strong></p>

3 <p>The binary system is a type of numerical system that we use to represent numbers with two digits: 0 and 1. The number 21 in binary is represented as 10101. It is a system of numerical data that computers use, as they operate with electric signals. In this topic, we are going to talk about 21 in binary.</p>

4 <h2>21 in Binary Conversion</h2>

5 <p>To get the<a>binary number</a><a>of</a>21, we need to divide 21 by 2 and record the<a>remainder</a>. It is done as below:</p>

6 <p>21 / 2 →<a>quotient</a>= 10, remainder = 1</p>

7 <p>10 / 2 → quotient = 5, remainder = 0</p>

8 <p>5 / 2 → quotient = 2, remainder = 1</p>

9 <p>2 / 2 → quotient = 1, remainder = 0</p>

10 <p>1 / 2 → quotient = 0, remainder = 1</p>

11 <p>Finally, we read the remainders from bottom to top and we get 10101 which is the binary number of 21.</p>

12 <h2>21 in Binary Chart</h2>

13 <p>To understand the binary of 21 let us look at the binary chart of<a>numbers</a>from 20 to 30:</p>

14 <strong>Numericals</strong><strong>Binary</strong>20 00010100 21 00010101 22 00010110 23 00010111 24 00011000 25 00011001 26 00011010 27 00011011 28 00011100 29 00011101 30 00011110<p>In the above chart, we see the binary conversions of numbers from 20 to 30. The above chart uses 8-bit notations for the binary numbers. We can represent the binary of 21 as 10101 or 00010101.</p>

15 <h2>How to Write 21 in Binary?</h2>

16 <p>We can write 21 in binary in two ways. We convert a<a>decimal</a>number to binary using the following two methods:</p>

17 <p><strong>Expansion Method:</strong></p>

18 <p>We use this method to break the number into sums of<a>powers</a>of 2</p>

19 <p><strong>Step 1:</strong>Identify the largest power of 2 that fits into 21 </p>

20 <p>List powers of 2 (starting from the largest power ≤ 21):</p>

21 <p>24 = 16 23 = 8 22 = 4 21 = 2 20 = 1</p>

22 <p><strong>Step 2:</strong>Now we find the largest power of 2 and break it down 21 = 16 + 4 + 1 This corresponds with the powers of 2:</p>

23 <p>24 = 16 22 = 4 20 = 1</p>

24 <p><strong>Step 3:</strong>Let us write the binary number:</p>

25 <p>Place 1 in positions where the power of 2 is used Place 0 in positions where it is not used Arrange the powers from highest to lowest: </p>

26 <p>24 23 22 21 20 = 10101</p>

27 <p>The final binary form is 10101</p>

28 <p><strong>Grouping Method:</strong></p>

29 <p>In this method we divide the number by 2, then we record the quotient, and read the remainders from bottom to top. </p>

30 <p><strong>Step 1:</strong>First, we have to divide 21 by 2 and record the quotient and remainder</p>

31 <p>21/2 = 10 remainder = 1</p>

32 <p>Record the remainder: 1</p>

33 <p><strong>Step 2:</strong>Divide the previous quotient (10) by 2 </p>

34 <p>10 / 2 = 5 Remainder = 0</p>

35 <p>Record the remainder: 0</p>

36 <p><strong>Step 3:</strong>Divide quotient 5 by 2 5 / 2 = 2 remainder = 1 Record the remainder: 1</p>

37 <p><strong>Step 4:</strong>Divide the previous quotient by 2</p>

38 <p>2 / 2 = 1 Remainder = 0</p>

39 <p>Record the remainder: 0</p>

40 <p><strong>Step 5:</strong>Divide 1 by 2</p>

41 <p>1 / 2 = 0 remainder = 1</p>

42 <p>Record the remainder: 1</p>

43 <p>Now we read the remainder from bottom to top:</p>

44 <p>So 21 in binary = 10101</p>

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47 <h2>Rules for Binary Conversion of 21</h2>

46 <h2>Rules for Binary Conversion of 21</h2>

48 <p>When converting 21 into binary, there are certain rules that must be followed. Some of the rules are as follows:</p>

47 <p>When converting 21 into binary, there are certain rules that must be followed. Some of the rules are as follows:</p>

49 <ul><li>Rule 1: Place Value Method </li>

48 <ul><li>Rule 1: Place Value Method </li>

50 <li>Rule 2: Division by 2 Method </li>

49 <li>Rule 2: Division by 2 Method </li>

51 <li>Rule 3: Representation Method </li>

50 <li>Rule 3: Representation Method </li>

52 <li>Rule 4: Limitation Rule</li>

51 <li>Rule 4: Limitation Rule</li>

53 </ul><p><strong>Rule 1: Place Value Method</strong></p>

52 </ul><p><strong>Rule 1: Place Value Method</strong></p>

54 <p>In this method we break down the number into a<a>sum</a>of powers of 2, in which each of them is represented by 1 in the corresponding binary position.</p>

53 <p>In this method we break down the number into a<a>sum</a>of powers of 2, in which each of them is represented by 1 in the corresponding binary position.</p>

55 <ul><li>Write the place values for binary (1, 2, 4, 8, 16, etc.)</li>

54 <ul><li>Write the place values for binary (1, 2, 4, 8, 16, etc.)</li>

56 </ul><ul><li>Determine how 21 can be represented using a<a>combination</a>of these place values.</li>

55 </ul><ul><li>Determine how 21 can be represented using a<a>combination</a>of these place values.</li>

57 </ul><ul><li>Assign 1 where the value is used for 21 and 0 where it does not.</li>

56 </ul><ul><li>Assign 1 where the value is used for 21 and 0 where it does not.</li>

58 </ul><ul><li>Arrange the binary digits in<a>sequence</a>from left to right.</li>

57 </ul><ul><li>Arrange the binary digits in<a>sequence</a>from left to right.</li>

59 </ul><p><strong>Rule 2: Division by 2 </strong></p>

58 </ul><p><strong>Rule 2: Division by 2 </strong></p>

60 <p>This method converts<a>decimal numbers</a>into binary numbers by repeatedly dividing by 2 and then we record the remainder.</p>

59 <p>This method converts<a>decimal numbers</a>into binary numbers by repeatedly dividing by 2 and then we record the remainder.</p>

61 <ul><li>Divide the number by 2 and then record the remainder as 0 or 1.</li>

60 <ul><li>Divide the number by 2 and then record the remainder as 0 or 1.</li>

62 </ul><ul><li>Repeat the process of dividing the quotients by 2 until the quotient is 0.</li>

61 </ul><ul><li>Repeat the process of dividing the quotients by 2 until the quotient is 0.</li>

63 </ul><ul><li>Then, read the binary numbers from bottom to top.</li>

62 </ul><ul><li>Then, read the binary numbers from bottom to top.</li>

64 </ul><p><strong>Rule 3: Representation Method</strong></p>

63 </ul><p><strong>Rule 3: Representation Method</strong></p>

65 <p>We use the representation method to convert a binary number to its decimal equivalent using positional values.</p>

64 <p>We use the representation method to convert a binary number to its decimal equivalent using positional values.</p>

66 <ul><li>A power of 2 is represented by each digit in the binary number, starting with the rightmost digit.</li>

65 <ul><li>A power of 2 is represented by each digit in the binary number, starting with the rightmost digit.</li>

67 </ul><ul><li>Multiply each digit with its corresponding power of 2.</li>

66 </ul><ul><li>Multiply each digit with its corresponding power of 2.</li>

68 </ul><ul><li>Sum all the results you get to get the decimal equivalent.</li>

67 </ul><ul><li>Sum all the results you get to get the decimal equivalent.</li>

69 </ul><p><strong>Rule 4: Limitation Rule</strong></p>

68 </ul><p><strong>Rule 4: Limitation Rule</strong></p>

70 <p>The limitation rule outlines the constraints when converting between binary and decimal systems.</p>

69 <p>The limitation rule outlines the constraints when converting between binary and decimal systems.</p>

71 <ul><li>Binary representation can only be done using digits like 0 and 1.</li>

70 <ul><li>Binary representation can only be done using digits like 0 and 1.</li>

72 </ul><ul><li>It must be made sure that the conversion accurately reflects the positional values.</li>

71 </ul><ul><li>It must be made sure that the conversion accurately reflects the positional values.</li>

73 </ul><ul><li>Make sure that no information is misinterpreted.</li>

72 </ul><ul><li>Make sure that no information is misinterpreted.</li>

74 </ul><h2>Tips and Tricks for Binary Numbers till 21</h2>

73 </ul><h2>Tips and Tricks for Binary Numbers till 21</h2>

75 <p>Binary is very easy to learn, but it can be quite confusing for students. Here are a few tips and tricks that students can use to master binary numbers:</p>

74 <p>Binary is very easy to learn, but it can be quite confusing for students. Here are a few tips and tricks that students can use to master binary numbers:</p>

76 <ul><li><strong>Divide and read:</strong>Divide the number by 2 and then write down the remainders in order. We then read the remainders from bottom to top for the correct binary numbers.</li>

75 <ul><li><strong>Divide and read:</strong>Divide the number by 2 and then write down the remainders in order. We then read the remainders from bottom to top for the correct binary numbers.</li>

77 </ul><ul><li><strong>Understanding the<a>base</a>-2 system:</strong>Just make sure to remember the base-2 system is the<a>number system</a>that uses only 2 digits (1 and 0). </li>

76 </ul><ul><li><strong>Understanding the<a>base</a>-2 system:</strong>Just make sure to remember the base-2 system is the<a>number system</a>that uses only 2 digits (1 and 0). </li>

78 </ul><ul><li><strong>Memorize certain binary numbers:</strong>Memorizing binary numbers can speed up conversions. 1 = 1, 2 = 10, 3 = 11, 10 = 1010, 20 = 10100.</li>

77 </ul><ul><li><strong>Memorize certain binary numbers:</strong>Memorizing binary numbers can speed up conversions. 1 = 1, 2 = 10, 3 = 11, 10 = 1010, 20 = 10100.</li>

79 </ul><h2>Common Mistakes and How to Avoid Them in 21 Binary Conversion</h2>

78 </ul><h2>Common Mistakes and How to Avoid Them in 21 Binary Conversion</h2>

80 <p>When learning about binary numbers, students might often make mistakes during conversions. Here are some common mistakes that students make and ways to avoid them:</p>

79 <p>When learning about binary numbers, students might often make mistakes during conversions. Here are some common mistakes that students make and ways to avoid them:</p>

81 <h3>Problem 1</h3>

80 <h3>Problem 1</h3>

82 <p>Convert 13 to binary</p>

81 <p>Convert 13 to binary</p>

83 <p>Okay, lets begin</p>

82 <p>Okay, lets begin</p>

84 <p>1101</p>

83 <p>1101</p>

85 <h3>Explanation</h3>

84 <h3>Explanation</h3>

86 <p>Divide 13 by 2 → Quotient = 6, Remainder = 1</p>

85 <p>Divide 13 by 2 → Quotient = 6, Remainder = 1</p>

87 <p>Divide 6 by 2 → Quotient = 3, Remainder = 0</p>

86 <p>Divide 6 by 2 → Quotient = 3, Remainder = 0</p>

88 <p>Divide 3 by 2 → Quotient = 1, Remainder = 1</p>

87 <p>Divide 3 by 2 → Quotient = 1, Remainder = 1</p>

89 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

88 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

90 <p>Read remainders from bottom to top → 1101</p>

89 <p>Read remainders from bottom to top → 1101</p>

91 <p>Well explained 👍</p>

90 <p>Well explained 👍</p>

92 <h3>Problem 2</h3>

91 <h3>Problem 2</h3>

93 <p>Convert 19 to binary using place value method</p>

92 <p>Convert 19 to binary using place value method</p>

94 <p>Okay, lets begin</p>

93 <p>Okay, lets begin</p>

95 <p>10011</p>

94 <p>10011</p>

96 <h3>Explanation</h3>

95 <h3>Explanation</h3>

97 <p>Identify the powers of 2 that sum to 19:</p>

96 <p>Identify the powers of 2 that sum to 19:</p>

98 <p>16+2+1=19</p>

97 <p>16+2+1=19</p>

99 <p>Assign 1 to the used powers and 0 to the unused ones:</p>

98 <p>Assign 1 to the used powers and 0 to the unused ones:</p>

100 <p>24 = 16 = 1</p>

99 <p>24 = 16 = 1</p>

101 <p>23 = 8 = 0</p>

100 <p>23 = 8 = 0</p>

102 <p>22 = 4 = 0</p>

101 <p>22 = 4 = 0</p>

103 <p>21 = 2 = 1</p>

102 <p>21 = 2 = 1</p>

104 <p>20 = 1 = 1</p>

103 <p>20 = 1 = 1</p>

105 <p>Arrange in order: 10011</p>

104 <p>Arrange in order: 10011</p>

106 <p>Well explained 👍</p>

105 <p>Well explained 👍</p>

107 <h3>Problem 3</h3>

106 <h3>Problem 3</h3>

108 <p>Convert 45 to binary by division by 2 method</p>

107 <p>Convert 45 to binary by division by 2 method</p>

109 <p>Okay, lets begin</p>

108 <p>Okay, lets begin</p>

110 <p>101101</p>

109 <p>101101</p>

111 <h3>Explanation</h3>

110 <h3>Explanation</h3>

112 <p>Divide 45 by 2 → Quotient = 22, Remainder = 1</p>

111 <p>Divide 45 by 2 → Quotient = 22, Remainder = 1</p>

113 <p>Divide 22 by 2 → Quotient = 11, Remainder = 0</p>

112 <p>Divide 22 by 2 → Quotient = 11, Remainder = 0</p>

114 <p>Divide 11 by 2 → Quotient = 5, Remainder = 1</p>

113 <p>Divide 11 by 2 → Quotient = 5, Remainder = 1</p>

115 <p>Divide 5 by 2 → Quotient = 2, Remainder = 1</p>

114 <p>Divide 5 by 2 → Quotient = 2, Remainder = 1</p>

116 <p>Divide 2 by 2 → Quotient = 1, Remainder = 0</p>

115 <p>Divide 2 by 2 → Quotient = 1, Remainder = 0</p>

117 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

116 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

118 <p>Read from bottom to top: 101101 </p>

117 <p>Read from bottom to top: 101101 </p>

119 <p>Well explained 👍</p>

118 <p>Well explained 👍</p>

120 <h3>Problem 4</h3>

119 <h3>Problem 4</h3>

121 <p>Convert 58 to binary</p>

120 <p>Convert 58 to binary</p>

122 <p>Okay, lets begin</p>

121 <p>Okay, lets begin</p>

123 <p>111010</p>

122 <p>111010</p>

124 <h3>Explanation</h3>

123 <h3>Explanation</h3>

125 <p>Break 58 into binary place values:</p>

124 <p>Break 58 into binary place values:</p>

126 <p>32 + 16 + 8 + 2 = 58</p>

125 <p>32 + 16 + 8 + 2 = 58</p>

127 <p>Assign 1 only to the used values, and put 0 for the unused values.</p>

126 <p>Assign 1 only to the used values, and put 0 for the unused values.</p>

128 <p>The binary is: 111010</p>

127 <p>The binary is: 111010</p>

129 <p>Well explained 👍</p>

128 <p>Well explained 👍</p>

130 <h3>Problem 5</h3>

129 <h3>Problem 5</h3>

131 <p>Convert 100 to binary</p>

130 <p>Convert 100 to binary</p>

132 <p>Okay, lets begin</p>

131 <p>Okay, lets begin</p>

133 <p>1100100</p>

132 <p>1100100</p>

134 <h3>Explanation</h3>

133 <h3>Explanation</h3>

135 <p>Divide 100 by 2 → Quotient = 50, Remainder = 0</p>

134 <p>Divide 100 by 2 → Quotient = 50, Remainder = 0</p>

136 <p>Divide 50 by 2 → Quotient = 25, Remainder = 0</p>

135 <p>Divide 50 by 2 → Quotient = 25, Remainder = 0</p>

137 <p>Divide 25 by 2 → Quotient = 12, Remainder = 1</p>

136 <p>Divide 25 by 2 → Quotient = 12, Remainder = 1</p>

138 <p>Divide 12 by 2 → Quotient = 6, Remainder = 0</p>

137 <p>Divide 12 by 2 → Quotient = 6, Remainder = 0</p>

139 <p>Divide 6 by 2 → Quotient = 3, Remainder = 0</p>

138 <p>Divide 6 by 2 → Quotient = 3, Remainder = 0</p>

140 <p>Divide 3 by 2 → Quotient = 1, Remainder = 1</p>

139 <p>Divide 3 by 2 → Quotient = 1, Remainder = 1</p>

141 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

140 <p>Divide 1 by 2 → Quotient = 0, Remainder = 1</p>

142 <p>Read the remainders from bottom to top = 1100100</p>

141 <p>Read the remainders from bottom to top = 1100100</p>

143 <p>Well explained 👍</p>

142 <p>Well explained 👍</p>

144 <h2>FAQs on 21 in Binary</h2>

143 <h2>FAQs on 21 in Binary</h2>

145 <h3>1.What is 21 in the binary number system?</h3>

144 <h3>1.What is 21 in the binary number system?</h3>

146 <h3>2.What is 21 in 8-bit binary?</h3>

145 <h3>2.What is 21 in 8-bit binary?</h3>

147 <p>In 8-bit binary we represent 21 as 00010101. Zeroes are added in the lead for 8-bit representations.</p>

146 <p>In 8-bit binary we represent 21 as 00010101. Zeroes are added in the lead for 8-bit representations.</p>

148 <h3>3.Where is binary used in the real-world?</h3>

147 <h3>3.Where is binary used in the real-world?</h3>

149 <p>We use binary, especially in computers as they use the binary number system to store<a>data</a>.</p>

148 <p>We use binary, especially in computers as they use the binary number system to store<a>data</a>.</p>

150 <h3>4.What if we add 1 to 10101 in binary?</h3>

149 <h3>4.What if we add 1 to 10101 in binary?</h3>

151 <p>If we add 1 to 10101, we get 10110, which is the binary number for 22.</p>

150 <p>If we add 1 to 10101, we get 10110, which is the binary number for 22.</p>

152 <h3>5.What is 2 × 10101 (21)</h3>

151 <h3>5.What is 2 × 10101 (21)</h3>

153 <p>So 10101 = 21,</p>

152 <p>So 10101 = 21,</p>

154 <p>So we multiply 21 × 2 = 42</p>

153 <p>So we multiply 21 × 2 = 42</p>

155 <p>42 in binary is: 101010.</p>

154 <p>42 in binary is: 101010.</p>

156 <h2>Important Glossaries for 21 in Binary</h2>

155 <h2>Important Glossaries for 21 in Binary</h2>

157 <ul><li><strong>Binary system:</strong>It is a base-2 system that uses only two digits, 0 and 1.</li>

156 <ul><li><strong>Binary system:</strong>It is a base-2 system that uses only two digits, 0 and 1.</li>

158 </ul><ul><li><strong>8-bit Representation:</strong>A way of representing numbers in binary using 8 binary digits.</li>

157 </ul><ul><li><strong>8-bit Representation:</strong>A way of representing numbers in binary using 8 binary digits.</li>

159 </ul><ul><li><strong>Place value:</strong>Place value is the position of a digit in a number. This position determines the value of the number.</li>

158 </ul><ul><li><strong>Place value:</strong>Place value is the position of a digit in a number. This position determines the value of the number.</li>

160 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

159 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

161 <p>▶</p>

160 <p>▶</p>

162 <h2>Hiralee Lalitkumar Makwana</h2>

161 <h2>Hiralee Lalitkumar Makwana</h2>

163 <h3>About the Author</h3>

162 <h3>About the Author</h3>

164 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

163 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

165 <h3>Fun Fact</h3>

164 <h3>Fun Fact</h3>

166 <p>: She loves to read number jokes and games.</p>

165 <p>: She loves to read number jokes and games.</p>