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April 16th, 2017, 04:19 AM  #1 
Newbie Joined: Nov 2016 From: iran Posts: 4 Thanks: 0  how do I convert binary to hexadecimal?
hi i wanted to know how to convert a binary(base 2) number to hexadecimal (base 16). i can do it by converting binary to decimal and decimal to hexadecimal but i want to know how i can do this conversion in one step. let's take 01100001 for example which equals to 97 in decimal and 61 in hexadecimal (i chose that number because every eight bit is one byte and if you show me how it's done using that number it would be much clearer. 
April 16th, 2017, 04:37 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,653 Thanks: 740  
April 16th, 2017, 05:23 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797 
16 (decimal) is (of course) 10 (hexadecimal) and 10000 (binary). Given any binary number, separate it into groups of 4 "bits" and convert each group to hexadecimal separately. For example, 10000 (binary) would be 1 and 0000. 1 (binary) is 1 (hexadecimal) and 0000 (binary) is 0 (hexadecimal). 10000 (binary) is 10 hexadecimal. For the numbers you give, 01100001 (binary), separate it to 0110 (binary) and 0001 (binary). 0110 (binary) is 0*8+ 1*4+ 1*2+ 0*1= 6 and 0001 (binary) is 0*8+ 0*4+ 0*2+ 1*1= 1 (obviously) so 01100001 (binary) is 61 (hexadecimal). Another example: 111001011010 separates as 1110, 0101, and 1010. 1110 is 1*8+ 1*4+ 1*2+ 0*1= 14 (D in hexadecimal), 0101 is 0*8+ 1*4+ 0*2+ 1*1= 5, and 1010 is 1*8+ 0*4+ 1*2+ 0*1= 10 (A in hexadecimal) so 111001011010 (binary) is D5A in hexadecimal. 
April 18th, 2017, 05:53 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,944 Thanks: 797  Quote:
 

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