How do you convert binary numbers to hexadecimal notation?

Answer 1

Each hexadecimal digit represent four binary bits. Using the table... 0 = 0000 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 A = 1010 B = 1011 C = 1100 D = 1101 E = 1110 F = 1110 ... replace each hexadecimal digit with its correspnding binary digits. As an example, 37AB16 is 00110111101010112.

Answer 2

If the number of bits in the binary value is not an exact multiple of four, pad the binary value with leading zeros. So 1010110100 becomes 001010110100. Split the binary value into groups of 4 bits: 0010, 1011 and 0100. Each group is a nybble (half-a-byte). Convert each nybble to its corresponding hexadecimal digit, as shown below:

0000 = 0x0

0001 = 0x1

0010 = 0x2

0011 = 0x3

0100 = 0x4

0101 = 0x5

0110 = 0x6

0111 = 0x7

1000 = 0x8

1001 = 0x9 1010 = 0xA

1011 = 0xB

1100 = 0xC

1101 = 0xD

1110 = 0xE

1111 = 0xF

Thus we get 0x2, 0xB and 0x4. Combining these hex digits in the same order we get 0x2B4, the hexadecimal equivalent of 1010110100.

Note that we can do the same thing to get the octal notation of a binary value, except we divide the binary value into groups of 3 bits, and convert as follows:

000 = 00

001 = 01

010 = 02

011 = 03

100 = 04

101 = 05

110 = 06

111 = 07

Thus 1010110100 becomes 001 010 110 100 which is 01264 in octal.

Note also that all bases that are a power of two (4, 8, 16, 32, 64 and so on), can be used to notate binary values. We use hexadecimal (base 16) simply because it reduces an 8-digit binary value to a 2-digit hexadecimal value which is much easier to notate. We use octal notation when the bit lengths are some multiple of 3 or when it is more notationally convenient to represent the value in groups of 3 bits, and use binary notation only when we're actually interested in the binary representation itself (the actual bits).

Answer 3

Start at the binary point (bp) - the binary equivalent of the decimal point.Group the binary digits into sets of four.

If there are not enough digits add one to three 0s furthest away from the bp.

The hexadecimal point will be in the same position as the binary point. And convert each binary quartet into the hexadecimal equivalent as follows:

0000 = 0 0001 = 1 0010 = 2 0011 = 3

0100 = 4 0101 = 5 0110 = 6 0111 = 7

1000 = 8 1001 = 9 1010 = A 1011 = B

1100 = C 1101 = D 1110 = E 1111 = F