Motorola MB68k-100, User Manual

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68000 Motherboard User’s Manual Rev. A
Page 8 of 54
numeral system is base 2, meaning that only these two digits are available. In base 2 the
significance of each digit’s place along a binary number differs by a factor of 2. When
written, binary numbers are expressed with a trailing subscript 2. Like in the base 10
system, the number 1
2
in binary represents a one. This is the ones place in the number,
2
0
. But binary 10
2
represents 2 or 2
1
, whereas in base 10 system 10
10
represents the
number ten or 10
1
. Binary 100
2
represents 4 or 2
2
. And 111
2
is a 7, 2
2
+2
1
+2
0
.
Another useful numeral system is base 16, known as hexadecimal. Hexadecimal simply
offers the advantage of grouping multiple binary digits together. Since the sixteen
possible combinations of four binary digits may be more concisely represented as a single
hexadecimal digit, hexadecimal is the preferred numeral system for its compactness.
Each hexadecimal digit represents four binary digits, and therefore two hexadecimal
digits represent a single 8-bit byte.
Table 1: Numeral Systems
Base
10
(Dec)
0 1 2 3 4 5 6 7 8 9 15 16
2
(Bin)
00000
2
00001
2
00010
2
00011
2
00100
2
00101
2
00110
2
00111
2
01000
2
01001
2
01111
2
10000
2
16
(Hex)
00
16
01
16
02
16
03
16
04
16
05
16
06
16
07
16
08
16
09
16
0F
16
10
16
As this relates to the computer, these binary digits physically correspond to the voltages
present on the signals within the computer. The digit 1 is typically represented by a high
voltage, while 0 is a low voltage. A succession of numbers over time in a digital system
appears as a signal waveform on the wire, with a separate parallel wire for each digit’s
place.
All data stored and processed in a computer can be thought of as numbers, encoded
through these voltage states. Whatever medium the data represents, it is a number
defined by parallel binary states to the computer. An image, for example, is defined
numerically as an array of values specifying how much red, green and blue to display at
each pixel location. Sound data numerically represents the amount to deflect a speaker
over time, which in turn creates corresponding sound waves. Text is defined numerically
by mapping the alphabet of possible characters to numerical codes. The message text
data is then broken into a string of characters, and the character at each position in that
string is defined by its numerical code. Using the ASCII coding standard as an example,
if 1 is added to the text data for the letter ‘A,’ it becomes a ‘B.’ If 32 is added to ‘A,’ it
becomes ‘a.’ To a computer, the world resolves to nothing more than numbers. These
numbers, though, have different meanings depending on which input or output device
they are associated. But within the computer, the numbers are simply electrical states of
the circuitry, carrying digital information.