082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

18 Chapter 1 Review of algebraic techniques
Engineeringapplication1.5
Seven-segmentdisplays
The number displays found on music systems, video and other electronic equipment
commonly employ one or more seven-segment indicators. A single sevensegment
indicator is shown in Figure 1.2(a). The individual segments are typically
illuminatedwithalight-emittingdiode(LED)orsimilaropticaldeviceandareeither
onoroff.ThesegmentsareilluminatedaccordingtothetableshowninFigure1.2(b),
where 1 indicates thatthe segment is turned on and 0 indicates thatitisturned off.
b.c.d.
number a b c d e f g
0000 1
1 1 1 1 1 0
0001
0 1 1 0 0 0 0
0010
1 1 0 1 1 0 1
a
0011
0100
1 1 1 1 0 0 1
0 1 1 0 0 1 1
f
g
b
0101
0110
1 0 1 1 0 1 1
1 0 1 1 1 1 1
e
d
c
0111
1000
1001
1 1 1 0 0 0 0
1 1 1 1 1 1 1
1 1 1 1 0 1 1
(a)
(b)
Figure1.2
(a) Seven-segment LED display. (b)Seven-segment coding.
The numbers in the microprocessor system driving the display are typically
stored in binary format, known as, binary coded decimal (b.c.d.). As an example
we consider displaying binary number 11101010 2
as a decimal number on sevensegment
displays. This represents the decimal number 234, which requires three
seven-segment displays.
Themicroprocessorfirstdividestheinputnumberby100andinthiscaseobtains
the result 2 with a remainder of 34. This can be done directly on the binary number
itself via a series of operations within the assembly language of the microprocessor
without first converting to a decimal number. The result 2 = 0010 2
is then decoded
usingFigure1.2(b),givingthebitpattern1101101whichispassedtothe‘hundreds’
display.
Theremainderof34isthendividedby10giving3withafinalremainderof4.The
number 3 = 0011 2
and so this can be outputted to the ‘tens’ display as the pattern
1111001. Finally, 4 = 0100 2
, which ispassed tothe display as the pattern 0110011.