MGMT 1030 Lecture Notes - Lecture 24: Radix, 5,6,7,8
6 May 2018
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MGMT 1030 Lecture 24 Notes – Nie’s decial represetatio
Introduction
• We will introduce a representation known as diminished radix complementary
representation
• So called because the value used as a basis for the complementary operation is
diminished by one from the radix, or base.
• Thus, base 10 diminished radix complementary representations use the value 9 as its
basis, and binary uses 1.
• Although the computer oiously uses the 1’s represetatio, e ill itrodue the 9’s
representation first
• Since we have found that it is easier for most students to understand these concepts in
the more familiar decimal system.
• Let us begin by considering a different means of representing negative and positive
integers in the decimal number system.
• Suppose that we manipulate the range of a three-digit decimal number system by
splitting the three-digit decimal range down the middle at 500.
• Arbitrarily, we will allow any number between 0 and 499 to be considered positive.
• Positive numbers will simply represent themselves.
• This will allow the value of positive numbers to be immediately identified.
• Numbers that begin with 5, 6, 7, 8, or 9 in the most significant digit will be treated as
representations of negative numbers.
• The shift in range.
• One convenient way to assign a value to the negative numbers is to allow each digit to
be subtracted from the largest numeral in the radix.
• Thus, there is no carry, and each digit can be converted independently of all others.
• Subtracting a value from some standard basis value is known as taking the complement
of the number.
• A representation known as diminished radix complementary representation
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