19.2 Conversions between Number System

19.2 Conversions between Number System Conversions between Denary, Binary, Octal and Hexadecimal Integers

From Denary Integers to Binary Integers Example 19.7 Convert 2710 into a binary integer.

Solution i.e. 2710 = 110112

From Binary, Octal or Hexadecimal Integers to Denary Integers Example 19.8 Convert 110112 into a denary integer.

Solution

i.e. 110112 = 1  24 + 1  23 + 0  22 + 1  21 + 1  20 = 16 + 8 + 0 + 2 + 1 = 2710

Example 19.9 Convert 2578 into a denary integer.

Solution

i.e. 2578 = 2  82 + 5  81 + 7  80 = 128 + 40 + 7 = 17510

Example 19.10 Convert 1A2B16 into a denary integer.

Solution

i.e. 1A2B16 = 1  163 + 10  162+ 2  161 + 11  160 = 4096 + 2560 + 32 + 11 = 6699

From Binary Integers to Octal Integers Example 19.11 Convert 10101112 into an octal integer.

Add leading zeros Solution 0 0 0 0 1 0 1 0 1 1 1 1 2 7  10101112 = 1278

From Binary Integers to Hexadecimal Integers Example 19.12 Convert 101011111112 into a hexadecimal integer.

Add leading zeros Solution 0 1 0 1 0 1 1 1 1 1 1 1 0 5 7 F  101011111112 = 57F16

From Hexadecimal Integers to Octal Integers Example 19.13 Convert 7DE16 into an octal integer.

Binary Octal Solution 7 D E Hexadecimal 0 1 1 1 1 1 0 1 1 1 1 0 3 7 3 6  7DE16 = 37368

From Octal Integers to Hexadecimal Integers Example 19.14 Convert 3678 into a hexadecimal integer.

Add leading zeros Binary Hexadecimal Solution 3 6 7 Octal 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 F 7  3678 = F716

The corresponding binary, octal and hexadecimal integers of denary integers 0 to 15:

Conversion between Decimal and Binary Fractions From Binary Fractions to Decimal Fractions

Example 19.15 Convert 0.11012 into a decimal fraction.

Solution 0.11012 = 1  2–1 + 1  2–2 + 0  2–3+ 1 2–4 = 0.812510

From Decimal Fractions to Binary Fractions Example 19.16 Convert 0.687510 into a binary fraction.

Solution

19.2 Conversions between Number System