Binary And Hexadecimal Numeration And Logical Operations Worksheet - Object Oriented Programming In Java, Marian Manyo Page 9
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12J A V A
L A B
M A N U A L
Similarly the six-bit binary numeral 110101 can be converted to binary by viewing it as
or 0011 0101, which is 35
11 0101
16
Hexadecimal to binary
To convert 5B
to binary, write each hexadecimal digit as a four – bit binary numeral.
16
If leading zeros are not needed, this is 1011011
5B
= 0101 1011
16
2
Hexadecimal to decimal
As with all place value numeration systems, a place value chart for hexadecimal numerals is
____
____
____
34
represents
3 · 16 + 4 · 1 = 52
16
AC
represents 10 · 16 + 12 · 1 = 172
16
256
16
1
F5
represents 15 · 16 + 5 · 1 = 245
16
16
16
16
2
1
0
Counting
To count in hexadecimal, you do not need to do any conversions. Just follow the same pattern that you
follow when counting in base 10 and base 2.
In base 10, the largest two – digit number is 99. 99 is followed by 100
In base 2, the largest two – digit number is 11. 11 is followed by 100
In base 16, the largest two – digit number is FF. FF is followed by 100
In base 16, counting from 95
:
16
96 97 98 99 9A 9B 9C 9D 9E 9F A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF B0
Answer the following questions.
E x e r c i s e 1 . 8
A. Rewrite the byte
in hex: __________________________________________________
11001001
B. Rewrite the hex numeral 6D in binary: ______________________________________________
C. For each of the hexadecimal numerals, write the next numeral. This is a counting question.
N
next N
N
next N
16
16
16
16
F
CF
C2
5F
CB
FFF
M A R I A N M A N Y O , M A R Q U E T T E U N I V E R S I T Y
P A G E 1 . 9
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