M68HC05 Family — Understanding Small Microcontrollers

Freescale Semiconductor, Inc...
Computer Numbers and Codes
Binary Coded Decimal
Freescale Semiconductor, Inc.
When mentally translating octal values to binary byte values, the octal
value is represented by three octal digits. Each octal digit represents
three binary bits so there is one extra bit (3 digits × 3 bits = 9 bits). Since
Western-speaking people typically work from left to right, it is easy to
forget to throw away the leftmost extra bit from the leftmost octal digit
and end up with an extra (ninth) bit. When translating from hexadecimal
to binary, it is easier because each hexadecimal digit translates into
exactly four binary bits. Two hexadecimal digits exactly match the eight
binary bits in a byte.
Binary coded decimal (BCD) is a hybrid notation used to express
decimal values in binary form. BCD uses four binary bits to represent
each decimal digit. Since four binary digits can express 16 different
physical quantities, there will be six bit-value combinations that are
considered invalid (specifically, the hexadecimal values A through F).
BCD values are shown with a $ sign because they are actually
hexadecimal numbers that represent decimal quantities.
When the computer does a BCD add operation, it performs a binary
addition and then adjusts the result back to BCD form. As a simple
example, consider the following BCD addition.
910 + 110 = 1010
The computer adds
0000 10012 + 0000 00012 = 0000 10102
But 10102 is equivalent to A16, which is not a valid BCD value. When the
computer finishes the calculation, a check is performed to see if the
result is still a valid BCD value. If there was any carry from one BCD digit
to another or if there was any invalid code, a sequence of steps would
be performed to correct the result to proper BCD form. The 0000 10102
is corrected to 0001 00002 (BCD 10) in this example.
M68HC05 Family — Understanding Small Microcontrollers — Rev. 2.0
34 Computer Numbers and Codes
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