Number Systems major part of mathematics. The number system and its conversions used in the various fields of mathematics and computer science. This article is about the binary, hexadecimal, and convert binary to the hexadecimal number system. The binary-to-decimal conversion very easy. The binary number system is a system in which numbers are expressed in the base 2. In the binary number system, the numbers are represented in terms of 0s and 1s only. The digits in the binary number system are called bits or binary digits. The hexadecimal number system is a system in which numbers are expressed in the base 16. In the hexadecimal number system, the numbers represented in terms of 0-9 and A – F. The hexadecimal number written as number H, (number)16, (number)H.
Conversion of Binary to Hexadecimal Number System
Method 1
◆ Then, Convert the obtained decimal into hexadecimal.
Let us understand this approach with the help of an example.
Consider a binary number (1101101)₂
So, its decimal conversion is
1 x 2⁶ + 1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 1 x 2² + 0 x 2¹ + 1 x 2⁰
=64 + 32 + 0 + 8 + 4 + 0 + 1
= (109)₁₀
Now, convert this to hexadecimal
The integer part of the number is (109)₁₀
Dividing (109 ÷ 16)₁₀
Gives 6 with remainder 13 (D)
Integer Remainder
109 ÷ 16 13 (D)
6 ÷ 16 6
0
Traverse the remainder column from bottom to top
(1101101)₂ = (6D)₁₆
Method 2
Direct Method for converting binary to hexadecimal
Take the given binary number and form the collection of four bits called a quad, then replace the quad with its hexadecimal equivalent. Hence, the obtained number is the conversion of a given binary to hexadecimal.
Note
- If, while forming the quad, the bits are before the radix point, then start forming the quad from the LSB bit and if the bits are after the radix point, start forming the quad from the immediate bit after the radix point.
- While forming the quad, the number of bits is less than 4 and before the radix point, then add 0s before the fewer bits to form a quad.
- While forming the quad, the number of bits is less than four and after the radix point, add 0s after the fewer bits to a quad.
Examples:-
Example 1 - (11101111.111001)₂ = (_______)₁₆
1110 1111. 1110 01
1110 1111 1110 0100
We added two zeros at the last as we have only 01, which does not make a quad. 0s are added after 01 because it is after the radix point.
E F E 4
(11101111.111001)₂ = (EF.E4)₁₆
Example 2 - Convert: (10111101.0001111)₂ = (_______)₁₆
Solution:
(10111101.0001111)2 = 1011 1101. 0001 1110 (The bold one 0 is added after 111 as 111 is after the radix point)
= B D 1 E
= (10111101.0001111)₂ = (BD.1E)₁₆
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Number Systems
