1. There is a relationship between binary, octal, and hexadecimal numbers. Binary is base 2, octal is base 8(23) and hexadecimal is base 16(24). Let's convert the binary number 101101011010111 to a hexadecimal number.

   Binary -> hexadecimal
   101101011010111

Starting at the rightmost digit, split the number into groups of 4
101 1010 1101 0111

2. Each of these groups has 4 binary digits that can range from 0 -15. This is exactly the value of one hexadecimal digit, so match each group of four bits with one hexadecimal digit.

Binary Number Groups Hexadecimal Equivalent  101 5 1010 A 1101 D 0111 7

So our binary number is equivalent to 5AD7₁₆. Going from hexadecimal reverses the procedure so each hexadecimal digit expands to 4 bits.

The same process occurs between octal and binary using only 3 bits.

Try the following conversions for practice:

10 110 1012 -> ___ ____ ____8
3F116 -> _____ _____ _____2
3528 -> _____ _____ _____2
482 ->____________2
482 -> ___________8
482 -> ________16
100012 -> _______10
57768 -> _______10
3DB16 -> _______10
110 111 0102 -> ___ ____ ____8
1011 0010 11112 -> ___ ____ ____16
3FA16 -> _____ ______ ______2
7128 -> ______ ______ ______2

The answers appear at the end of this lesson.