Hexadecimal Numbers

Review

Memory contains:

f800:  40
f801:  97
f802:  12
f803:  0d

PC contains f801, A contains 24. What happens?

What is 43 in binary? 101011

Hexadecimal numbers

Problem with binary: writing all those 1's and 0's gets tedious. But notice that four bits is capable of representing a number from 0 to 15. This means that we can ``scoop up'' groups of 4 bits and treat them as numbers in base 16 (hexadecimal, or hex). Does it work? Let's convert 43 to hex. We get 2,11. Another problem! We don't have enough digits. So, we use a=10, b=11, and so forth to f=15 when we're working in hex. Now, we can go back and look at those screwy numbers we've been using -- what's f800 in binary? How about decimal?

As you might expect, we can indeed do addition in hexadecimal. So, what would


 3592
+4f9a

be?

Radix conversions: decimal, hex, binary

Here's a table, showing the translations between the common number bases for the first sixteen numbers.

Decimal Hexadecimal Octal Binary
0 0 0 0000
1 1 1 0001
2 2 2 0010
3 3 3 0011
4 4 4 0100
5 5 5 0101
6 6 6 0110
7 7 7 0111
8 8 10 1000
9 9 11 1001
10 a 12 1010
11 b 13 1011
12 c 14 1100
13 d 15 1101
14 e 16 1110
15 f 17 1111