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Decimal / Hexadecimal Conversion

Hexadecimal Number System [Base-16]

The hexadecimal number system uses sixteen values to represent numbers. The values are,

0 1 2 3 4 5 6 7 8 9 A B C D E F

with 0 having the least value and F having the greatest value. Columns are used in the same way as in the decimal system, in that the left most column is used to represent the greatest value.

As we have seen in the decimal system, the values in the set (0 and 1) repeat, in both the vertical and horizontal directions.

0 - F, 10 -1F, 20 - 2F, 30 - 3F ......

Hexadecimal is often used to represent values [numbers and memory addresses] in computer systems.

|Decimal - Binary - Hexadecimal |

|Decimal |Binary |Hexadecimal |

|0 |0000 |0 |

|1 |0001 |1 |

|2 |0010 |2 |

|3 |0011 |3 |

|4 |0100 |4 |

|5 |0101 |5 |

|6 |0110 |6 |

|7 |0111 |7 |

|8 |1000 |8 |

|9 |1001 |9 |

|10 |1010 |A |

|11 |1011 |B |

|12 |1100 |C |

|13 |1101 |D |

|14 |1110 |E |

|15 |1111 |F |

Converting decimal to hexadecimal

Problem: Convert 232 decimal to hexadecimal.

Use the method used earlier to convert decimal to binary, but divide by 16 instead of by 2.

232 / 16 = 14 with a remainder of 8

14 / 16 = 0 with a remainder of E (14 decimal = E)

= E816

Another method is to convert the decimal value into a binary number, and then convert that result as shown below.

Converting hexadecimal to decimal

Problem: Convert 176 in hexadecimal to decimal.

Each column represents a power of 16,

176 =

---- 6 * 160 = 6

----- 7 * 161 = 112

------ 1 * 162 = 256

----

374

Converting binary to hexadecimal

Problem: Convert 10110 to hexadecimal.

Each hexadecimal digit represents 4 binary bits. Split the binary number into groups of 4 bits, starting from the right. In this case, 10110 is equivalent to 00010110, so we can split the binary number like this:

0001 0110

The left group, 0001, is equal to 1.

The right group, 0110, is equal to 6.

Because both digits are less than ten, we can simply combine them for the answer.

= 16 in hexadecimal, or 1616

To avoid confusion, we often add a suffix to indicate the number base

162h h means hexadecimal 16216 16 means base 16

162d d means decimal 16210 10 means base 10

162o o means octal 1628 8 means base 8

101b b means binary 1012 2 means base 2

Sample Problems for Hexadecimal Conversion

In each case, don’t simply convert the value, but consider which value cannot be the solution, thus narrowing the choices and making your job easier.

1. 1010101b in hexadecimal is

__ 6616

__ 5516

__ 4416

__ 64516

2. 1000100b in hexadecimal is

__ 4416

__ 3316

__ 4316

__ 3416

3. 0010010b in hexadecimal is

__ 1116

__ 2216

__ 2116

__ 1216

4. 0111101b in hexadecimal is

__ 3D16

__ DE16

__ F316

__ 0916

5. BCD16 in decimal is

__ 213210

__ 321010

__ 302110

__ 102310

6. AF16 in decimal is

__ 71510

__ 7110

__ 5710

__ 17510

7. 9216 in decimal is

__ 6410

__ 14610

__ 1610

__ 4110

8. 7E16 in decimal is

__ 12610

__ 12710

__ 7110

__ 114d

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