Motorola M6800 User Manual download pdf (Page 21)

MPU-21

101111

= lx2

+ 1x2

+ lx2

+ 0x2

+ 1x2

= 1x1 + 1x2 + 1x4 + 1x8 + 0x16 + 1x32

= 1 + 2 + 4 + 8 + 0 + 32

= 47

In general, converting from a number in any base to a number in base

10 is accomplished as follows:

+ A

-- -- -- -- A

)

where B is the base of the number system and A is the particular digit in the

original number corresponding to its position to the left of the decimal

point. On the example just completed, (101111). A

= 1, A

1, A

= 0, & A

= 1 and B = 2 (base 2).

Another base which is very convenient in digital computers is base

8, since base 8 is really a convenient way of representing base 2. Lets

illustrate by converting a base 10 number to base 8 & base 2. Let's convert

61 in base 10 to a number in base 8 and a number in base 2. By continuous

division:

61 R=5

7 R=7 75

61 R=1

30 R=0

15 R=1

7 R=1 111101

3 R=1

1 R=1

1 ... 20 21 22 23 24 25 26 27 28 29

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Motorola M6800 User Manual Page 21