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Motorola M6800 User Manual

Page 20

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MPU-20

Number Systems

Everyone is quite familiar with the base 10 number system i.e. 0, 1,

2, 3, 4, 5, 6, 7, 8, & 9, since this is the system we all use day to day. Let

us review a typical number, say 2743, and see what it really means. The least

significant digit (LSD) is 3 and the most significant digit (MSD) is 2. Since

we are talking about a base 10 number, the number 2743 really is

= 3x100 + 4x101 + 7x102 + 2x103

= 3x1 + 4x10 + 7x100 + 2x1000

= 3 + 40 + 700 + 2000

= 2743.

In digital computers, base 10 numbers are represented in binary

form, i.e. 1's & 0's. Lets take a base 10 number and convert it to a binary

(base 2) number. A method of doing this is known as "repeated division by ?".

The base 10 number of 47 is converted to binary as shown below:

23

2 47

R=1

11

2 23

R=1

5

2 11

R=1

2

2 5

R=1

1011112

2

2 2

R=0

0

2 1

R=1

Converting 1011112 back to our base 10 number is done in the same

manner as above