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Working with Numbers: Binary and Hexadecimal 813

A

Hexadecimal ........................................................................................................

Because binary numbers are difficult to read, a simpler way to represent the same values

is sought. Translating from binary to base 10 involves a fair bit of manipulation of num-

bers; but it turns out that translating from base 2 to base 16 is very simple, because there

is a very good shortcut.

To understand this, you must first understand base 16, which is known as hexadecimal.

In base 16, there are sixteen numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

The last six are arbitrary; the letters A–F were chosen because they are easy to represent

on a keyboard. The columns in hexadecimal are

Column 4321

Power 163 162 161 160

Value 4096 256 16 1

To translate from hexadecimal to decimal, you can multiply. Thus, the number F8C

represents:

F * 256 = 15 * 256 = 3840

8 * 16 = 128

C * 1 = 12 * 1 = 12

3980

(Remember that F in Hexadecimal is equal to 15 10 .)

Translating the number FC to binary is best done by translating first to base 10, and then

to binary:

F * 16 = 15 * 16 = 240

C * 1 = 12 * 1 = 12

252

Converting 252 10 to binary requires the chart:

Column 987654321

Power 28 27 26 25 24 23 22 21 20

Value 2561286432168421

There are no 256s.

1*128 = 128. 252-128 = 124

1*64 = 64. 124-64 = 60

1*32 = 32. 60-32 = 28

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