Page 19 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Digital Circuits and Logic Design

Notes

2AB =? 2
16
Solution:
Step 1: Convert decimal equivalent each hexadecimal digit to 4 binary digits.

2 = 2 = 0010
16 10 2
A = 10 = 1010 2
10
16
B = 11 = 1011
16 10 2
Step 2: Combine the binary groups.
0010 0010 1011
2AB =
16 2 A B
Hence, 2AB = 001010101011
16 2
Table 1.4 summarizes the relationship among decimal, hexadecimal, binary, 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 we substitute octal digits for binary digits, the substitution is on a one-
to-three basis. Hence, computers that print octal numbers instead binary, while taking memory
dump, save one-third of printing space and time.

Similarly, note that the maximum value of one digit in hexadecimal is equal to the maximum
value of four digits in binary. Hence, 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 one-to-four
reduction in space and time required for memory dump.
Table 1.4: Relationship among Decimal, Hexadecimal, Binary, and Octal Number Systems

Decimal Hexadecimal Binary Octal
0 0 0 0
1 1 1 1
2 2 10 2
3 3 11 3
4 4 100 4
5 5 111 5
6 6 110 6
7 7 111 7
8 8 1000 10
9 9 1001 11
10 A 1010 12
11 B 1011 13
12 C 1100 14
13 D 1101 15
14 E 1110 16
15 F 1111 17
16 10 10000 20

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