Short Cuts Between Binary, Octal, and Hexadecimal

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

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.

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.