MGMT 1000 Lecture Notes - Lecture 17: Binary Number, Hexadecimal
MGMT 1000 Lecture 17 Notes – Conversion
Introduction
• In fact, with a bit of practice, the conversion can be done mentally and the answer
written down directly.
• These conversions work because a grouping of several digits in the smaller number base
corresponds, or maps, exactly to a single digit in the larger number base.
• Two particularly useful examples for computer work are the cases of conversion
between base 2 and base 8 and conversion between base 2 and base 16.
• Since 8=23, we can represent binary numbers directly in base 8 using one octal digit to
correspond to each three binary digits.
• Similarly, it takes one hexadecimal digit to exactly represent 4 bits.
• The advantage of representing binary numbers in hexadecimal or octal is obvious
• It is clearly much easier to read and manipulate four-digit hexadecimal numbers than
16-bit binary numbers.
• Since the conversion between binary and octal and hexadecimal is so simple, it is
common to use hexadecimal or octal representation as a shorthand notation for binary.
• Note that base 8 and base 16 are not directly related to each other by power, but
conversion could be performed easily by using base 2 as an intermediary.
• Since the correspondence of binary and octal or hexadecimal is exact, the conversion
process simply consists of breaking the binary number into groups of three or four,
starting from the least significant bit (the unit bit), and converting each group
independently.
• It may be necessary to mentally add 0s to the left end of the number to convert the
most significant digit.
• This is most easily illustrated with an example
• EXAMPLE
• Let us convert 11010111011000 to hexadecimal.
• Grouping the binary number by fours, we have 0011 0101 1101 1000 or 35D816
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