Motorola M6800 - Manual (Page 21)

MPU-21
1011112 = lx2
0 + 1x21 + lx22 + lx23 + 0x24 + 1x25
= 1x1 + 1x2 + 1x4 + 1x8 + 0x16 + 1x32
= 1 + 2 + 4 + 8 + 0 + 32
= 4710
In general, converting from a number in any base to a number in base
10 is accomplished as follows:
(A0 B
0 + A
1 B
1 + A
2 B
2 + A
3 B
3 + A
4 B
4 -- -- -- -- A
n B
n)
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). A0 = 1, A1 = 1, A2 = 1, A3 =
1, A4 = 0, & A5 = 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:
7
8 61 R=5
0
8 7 R=7 758
30
2 61 R=1
15
2 30 R=0
7
2 15 R=1
3
2 7 R=1 1111012
1
2 3 R=1
0
2 1 R=1