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11-6 Base Conversions and Arithmetic and Logic
The Representation of Numbers
Although the display of a number is converted when the base is changed, its stored
form is not modified, so decimal numbers are not truncated — until they are used in
arithmetic calculations.
When a number appears in hexadecimal, octal, or binary base, it is shown 36 bits
(12 octal digits or 9 hexadecimal digits). Leading zeros are not displayed, but they
are important because they indicate a positive number. For example, the binary
representation of 125
10
is displayed as:
1111101b
which is the same as these 36 digits:
000000000000000000000000000001111101b
Negative Numbers
The leftmost (most significant or "highest") bit of a number's binary representation is
the sign bit; it is set (1) for negative numbers. If there are (undisplayed) leading
zeros, then the sign bit is 0 (positive). A negative number is the 2's complement of
its positive binary number.
()
()
b
Changes to base 2; BIN
annunciator on. This
terminates digit entry, so no
is needed between
the numbers.
Result in binary base.
()
Result in hexadecimal base.
()
Restores decimal base.
Keys: Display: Description:
()
Enters a positive, decimal
number; then converts it to
hexadecimal.