MGMT 1000 Lecture Notes - Lecture 2: Binary Number
MGMT 1000 Lecture 2 Notes – Number systems number
Introduction
• As humans, we generally count and perform arithmetic using the decimal or base 10,
number system.
• The base of a number system is simply the number of different digits, including zero that
exist in the number system.
• In any particular set of circumstances, a particular base might be chosen for
convenience, efficiency, technological, or any other reasons.
• Historically, it seems that the main reason that we use base 10 is that humans have ten
fingers, which is as good a reason as any.
• Any number can be represented equivalently in any base, and it is always possible to
convert a number from one base to another without changing its meaning.
• Computers perform all of their operations using the binary or base 2, number system.
• All program code and data are stored and manipulated in binary form.
• Calculations are performed using binary arithmetic.
• Each digit in a binary number is known as a bit (for binary digit) and can have only one of
two values, 0 or 1.
• Bits are commonly stored and manipulated in groups of 8 (known as a byte), 16 (usually
known as a half word), 32 (a word), or 64 bits (a double word). Sometimes other
groupings are used.
• The number of bits used in calculations affects the accuracy and size limitations of
numbers manipulated by the computer.
• And, in fact, in some programming languages, the number of bits used can actually be
specified by the programmer in declaration statements.
• In the programming language Java, for example, the programmer can declare a signed
integer variable to be short (16 bits), int (32 bits)
• Long (64 bits) depending on the anticipated size of the number being used and the
required accuracy in calculations.
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