This document discusses two methods for converting hexadecimal numbers to binary numbers. Method 1 involves first converting the hexadecimal number to decimal, and then converting the decimal to binary. Method 2 involves converting each hexadecimal digit directly to its 4-bit binary equivalent. Examples are provided to demonstrate converting individual hexadecimal numbers and portions of numbers to binary.

1. Conversion of a hexadecimal number to a binary
number
METHOD 1
First it should be converted to its equivalent
decimal number
Then convert the decimal number so obtained
to its binary equivalent
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2. METHOD 2
Each digit of the given hexadecimal number should be
converted to its 4-bit binary equivalent
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3. 1.Convert the hexadecimal number ABC to its
equivalent binary number
 METHOD 1
(ABC)16 = A *162 + B*161 + C*160
= 10 *256 + 11*16 + 12*1
= 2560 + 176 + 12
= (2748)10
(1010 1011 1100)10
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4. Now converting this decimal into binary
Division Remainders
2 2748
2 1374 0
2 687 0
2 343 1
2 171 1
2 85 1
2 42 1
2 21 0
2 10 1
2 5 0
2 2 1
2 1 0
2 0 1
Thus (ABC)16 = (2748)10 = (101010111100)
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5. METHOD 2
A16 = (10)10 = (1010)2 2 10
B16 = (11)10 = (1011)2 2 5 0
C16 = (12)10 = (1100)2 2 2 1
2 1 0
0 1
(10)10 = (1010)2
(ABC)16 = ( 1010 1011 1100 )2
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6. 2. Convert the hexadecimal number 6B9 to its
equivalent binary number
 Each digit of the given hexadecimal number is
converted to its 4-bit binary equivalent
(6B9)16 = (0110) (1011)(1001)
= (011010111001)2
= (011010111001)2
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7. 3. Convert the hexadecimal number 6D.3A to its
equivalent binary number
 Each digit of the given hexadecimal number is
converted to its 4-bit binary equivalent
(6D.3A)16 = (0110) (1101) . (0011) (1010)
=(01101101.00111010)2
=(1101101.0011101)2
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8. Summary
In this class, you have learnt about
 Conversions of binary number to hexadecimal
 Conversions of hexadecimal to binary number
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9. Frequently Asked Questions
 Explain how to convert a binary number to
equivalent hexadecimal
 Explain how to convert a hexa decimal number to
equivalent binary
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10. Quiz
 The binary equivalent of (ABC)
a. 1010 1011 1100
b.1010 1100 1100
c. 1011 1010 1101
Answer: a
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