Binary, Denary, hexadecimal and base 10

1. Binary, Denary, hexadecimal and base 10 By Tim Conlan

2. Converting between binary and hexadecimal • You first split the binary into two nibbles, you then work out the number for each nibble… for example, 10111011 goes to 1011|1011, this is 11 on each side and 11 in hex is B, so the answer is BB

3. Hex to Binary/Base 10. • BC: to do this you must first know what each letter represents, B is 11 and C is 12, you need to separate the 8 bit into two nibbles. 11 is 1011 and 12 1100, so the full number is 10111100 and from here on converting back into base 10 Is simple, 128 64 32 16 8 4 2 1. • The final answer is 188.

4. Hex • Large binary numbers are quite difficult to remember and when programmers work with these values they need something that is easier to recognise and appreciate. Converting everything from base 2 to base 10 and back is quite complex and we need something that still uses base 2 but is easier to understand,, since a byte as 8 bits it easily splits into 2 nibbles with 4 bits each. If we look at our column headings for a 4-bit number we see that we can represent the range of numbers 0 to 15

5. Converting from base 10 to 16 • Converting from base 10 to base 16 can be done using the same methods we identified for converting base 10 to base 2: • Divide by 16 repeatedly and record the remainders. • Converting 45 in base 10 to base 16: 45/16=14 r 11(B) 14/16=0 r 2 Therefore 45 in base 10 = 2D in base 16.