Page 81 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

62 Chapterseven

The rules for counting in octal and hexadecimal are the same as for any
other place-value system-when all the digits in a column are exhausted, the
next count sets that column to zero and increments the column to the left
(Figure 7-15).
Although not strictly necessary, binary, octal and hexadecimal numbers are
often prefixed by leading zeros to pad them to whatever width is required. This
padding is usually performed to give some indication as to the physical number
of bits used to represent that value within a computer.
Each octal digit can be directly mapped onto three binary digits, and each
hexadecimal digit can be directly mapped onto four binary digits (Figure 7-16).

Decimal Binary Octal Hexadecimal
0 00000000 000 00
1 00000001 00 1 01
2 000000 10 002 02
3 0000001 1 003 03
4 000001 00 004 04
5 000001 0 1 005 05
6 00000110 006 06
7 000001 1 1 007 07
8 00001000 01 0 08
9 00001 001 01 1 09
10 0000101 0 012 OA
11 00001011 013 06
12 00001100 0 14 oc
13 00001101 015 OD
14 0000 11 10 016 OE
15 0000 11 11 017 OF
16 00010000 020 10
17 00010001 021 11
18 0001 001 0 022 12

etc . etc. etc. etc.

Figure 7-1 5. Counting in octal and hexadecimal