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Unformatted text preview: 4+0+1
= 1310
= D16
00112 = 0 x 23 + 0 x 22 + 1 x 21 + 1 x 2°
=0+0+2+1 = 316
Hence, 110100112
= D3,6
Compare the result with the result of Example 3.17.
Shortcut Method for Hexadecimal to Binary Conversion
The following steps are used in this method:
Step 1: Convert the decimal equivalent of each hexadecimal digit to 4 binary digits.
Step 2: Combine all the resulting binary groups (of 4 digits each) into a single binary
number.
Example 3.24.
2AB16 = ?2
Solution:
Step 1: Convert the decimal equivalent of each hexadecimal digit to 4 binary digits.
216 = 210 = 00102 A16=10I0 =10102
B16=ll10 =l0ll2
Step 2: Combine the binary groups.
2AB16 = 0010/2 1010/A 1011/B
Hence, 2AB16 = 0010101010112
Figure 3.2 summarizes the relationship between the decimal, binary, hexadecimal, and
octal number systems. Note that the maximum value for a single digit of octal (7) is equal
to the maximum value of three digits of binary. The value range of one digit of octal
duplicates the value range of three digits of binary. If octal digits are substituted for
binary digits, the substitution is on a onetothree basis. Thus, computers that print octal
numbers instead of binary, while taking memory dump, save onethird of the printing
space and time.
Decimal
Hexadecimal
Binary
Octal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
10 0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
Mi
10000 0
1
2
3
4
5
6
7
10 Figure 3.2. Relationship among Decimal, Binary, Hexadecimal and Octal number
systems.
Similarly, note that the maximum value of one digit in hexadecimal is equal to the
maximum value of four digits in binary.
Thus, the value range of one digit of
hexadecimal is equivalent to the value range of four digits of binary.
Therefore,
hexadecimal shortcut notation is a onetofour reduction in the space and time required
for memory dump.
FRACTIONAL NUMBERS In binary number system, fractional numbers are formed in the same general way as in
the decimal number system. For example, in the decimal number s...
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 Spring '14

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