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

1.3 Number bases 19
The display shows
a
a
a
f
g
b
f
g
b
f
g
b
e
d
c
e
d
c
e
d
c
Notice that prior to decoding for display, by successive division by 100 and 10
the number has been converted into separate b.c.d. digits. Integrated circuits are
available which convert b.c.d. directly into the bit patterns for display. Hence the
output bit pattern of the microprocessor may be chosen to be b.c.d. In this case it
has the advantage that fewer pins are required on the microprocessor to operate the
display.
EXERCISES1.3
1 Convert the following decimal numbersto binary
numbers:(a) 19 (b)36 (c) 100 (d)796
(e)5000
2 Convert the following binarynumbers to decimal
numbers:(a) 111 (b)10101 (c) 111001
(d)1110001 (e) 11111111
3 What isthe highestdecimal number that can be
written in binary formusingamaximum of(a)2
binarydigits (b)3binarydigits (c)4binary digits
(d)5binary digits? Canyou spotapattern? (e)Write
aformulaforthe highest decimal number that can be
written usingN binary digits.
4 Writethe decimal number 0.5 in binary.
5 Convert the following hexadecimal numbersto
decimal numbers:(a)91 (b)6C (c)A1B (d)F9D4
(e)ABCD
6 Convert the following decimal numbersto
hexadecimal numbers:(a)160 (b)396 (c)5010
(d)25000 (e)1000000
7 Calculate the highestdecimal number that can be
represented byahexadecimal number with (a)1digit
(b)2digits (c)3digits (d)4digits (e)N digits
8 Expressthedecimalnumber375asbothapurebinary
number and anumber in b.c.d.
9 Convert (a)1111111 2 (b)101010111 2 into
hexadecimal.
Solutions
1 (a) 19 10 =10011 2 (b) 100100 (c) 1100100
(d) 1100011100 (e) 1001110001000
2 (a)111 2 = 7 (b)21 (c) 57 (d)113 (e)255
3 (a)3 (b)7 (c) 15 (d)31 (e) 2 N −1
4 Thebinarysystem is basedonpowers of2. The
examples in the text can be extended to the case of
negative powers of2justasin the decimal system
numbersafterthe decimal place represent negative
powers of10.So, forexample, the binarynumber
11.101 2 isconverted to decimal asfollows:
11.101 2 =1×2 1 + 1×2 0 + 1×2 −1
+0×2 −2 +1×2 −3
=2+1+ 1 2 + 1 8
= 3 5 8