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6 Assembly Language Programming for the 68000 Family

Binary

Virtually all computers use 2 as the base for numerical quantities.

The choice of 2 as a base for computers is not arbitrary. Internally, the

electrical elements, or gates, that collectively construct the computer are

much easier to build if they are required to represent only two values or

states, they are thus called binary state devices. Each element can only

represent the values zero or one. Each one or zero is called a bit, or binary

digit. In order to represent larger numbers, bit positions must be used.

Binary numbers are based on powers of two rather than on powers of

ten. For example, the binary number “1011” is equivalent to:

1(2)3+0(2)2+l(2 >1+1(2)0

This value is equivalent to:

8+0+2+1 = 11

in decimal representation. The positional values of the bits are thus:

(2)°

(2)1

(2) 2

(2)3

(2) 4

<2)16 = 65,536

etc.

To convert a binary number to its decimal equivalent, merely add up

the appropriate powers of two. If the binary position contains a 1, the

decimal value of that bit position is added.

Conversions

Converting a decimal number to binary is not quite as simple as con

verting a binary number to decimal. One method is to work backwards.

1 2 ... 15 16 17 18 19 20 21 22 23 24 25 ... 255 256

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