Motorola M68000 User's Guide download pdf (Page 23)

Mumber 5ystems 9

To convert from hex to binary we merely write the equivalent of each

hex digit in binary. To convert 6E3Cie to binary we would write:

6 e 3 c

0110 1110 0011 1100

and our binary equivalent is IIOIIIOOOIIIIOO2. We can go from binary

to hex in the same manner. IIIIOOOOIOIO2 is F0Ai6.

Arithmetic in Binary and Hexadecimal

We can perform the normal arithmetic operations of addition, sub

traction, multiplication, and division in any number base. Addition and

subtraction are simple if we remember that a carry or borrow may be

required. If the sum of two digits equals or exceeds the number base, a

carry is generated. The value used as the carry or borrow is equal to the

number base. For example, if we add two binary numbers together, we

generate a carry if the sum of the bits in one binary position and a pos

sible carry from the next lowest position is greater than or equal to two.

Adding 11001012 to OIIIIOI2 gives us:

1100101

+ 0111101

10100010

Let’s try adding 72A816 to IF08i6.

72A8

+ 1F08

91B0

Subtraction is only slightly more difficult. If the individual digits

cannot be subtracted from one another, we need to borrow from the

next higher digit position. In other words, if the minuend (top digit) is

less than the subtrahend (bottom digit) we need a borrow. In binary the

value borrowed is always two. This borrow is added to the minuend, the

subtraction is then performed on the two digits. To adjust for the borrow,

just as we had to adjust for a carry, we must add one to the subtrahend

in the next higher digit position. For example, in binary

n i l 1001

- 0110 - 0110

1001 0011

1 2 ... 18 19 20 21 22 23 24 25 26 27 28 ... 255 256

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Motorola M68000 User's Guide Page 23