Page 28 - ARM 64 Bit Assembly Language

Introduction 11

0
14 → 3 →
4 56 4 14 4 3
40 12
16 2
16
0

Reading the remainders from right to left yields: 320 4 . This result can be double-checked by
converting it back to base ten as follows:

2
1
320 4 = 3 × 4 + 2 × 4 + 0 × 4 0
= 48 + 8 + 0
= 56 10 .
Since we arrived at the same number we started with, we have verified that 56 10 = 320 4 .This
conversion procedure works for converting any integer from base ten to any arbitrary base b.
Example 2 gives another example of converting from base ten to another base b.
Example 2. Converting from base ten to an arbitrary base.

Converting 8341 10 to base seven is accomplished as follows:
0
1191 → 170 → 24 → 3 →
7 8341 7 1191 7 170 7 24 7 3
7000 700 140 21
1341 491 30 3
700 490 28
641 1 2
630
11
7
4
8341 10 = 33214 7

1.3.2.3 Bases that are powers-of-two

In addition to the methods above, there is a simple method for quickly converting between
base two, base eight, and base sixteen. These shortcuts rely on the fact that two, eight, and
sixteen are all powers of two. Because of this, it takes exactly four binary digits (bits) to rep-
resent exactly one hexadecimal digit. Likewise, it takes exactly three bits to represent an octal