Chapter_2(S)

# Chapter_2(S) - BinaryNumberSystems PositionalNotation 104...

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Binary Number Systems

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Positional Notation 10 4 10 3 10 2 10 1 10 0 10000 1000 100 10 1 Allows us to count past 10. Each column of a number represents a power of the base. The exponent is the order of magnitude for the column.
Positional Notation 10 4 10 3 10 2 10 1 10 0 10000 1000 100 10 1 The Decimal system is base d on the number of digits we have.

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Positional Notation 10 4 10 3 10 2 10 1 10 0 10000 1000 100 10 1 The magnitude of each column is the base , raised to its exponent .
Positional Notation 10 4 10 3 10 2 10 1 10 0 10000 1000 100 10 1 2 7 9 1 6 2 0000 + 7 000 + 9 00 + 1 0 + 6 =27916 The magnitude of a number is determined by multiplying the magnitude of the column by the digit in the column and summing the products.

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Binary Numbers The base in a Binary system is 2. There are only 2 digits – 0 and 1 . Since we use the term frequently, “ b inary dig it can be shortened to ‘ bit ’. 8 bits together form a byte .
A Single Byte 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 1 1 1 1 1 1 1 1 128 +64 +32 +16 +8 +4 + 2 + 1 =255

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A Single Byte 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 1 1 1 1 1 1 1 1 128 +64 +32 +16 +8 +4 + 2 + 1 =255
A Single Byte 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 1 1 1 1 1 1 1 1 128 +64 +32 +16 +8 +4 + 2 + 1 =255

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A Single Byte 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 1 1 1 1 1 1 1 1 128 +64 +32 +16 +8 +4 + 2 + 1 =255 is the largest decimal value that can be expressed in 8 bits.
A Single Byte 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 0 0 0 0 0 0 0 0 0 +0 +0 +0 +0 +0 + 0 + 0 = 0 There is also a representation for zero , making 256 (2 8 ) combinations of 0 and 1 in 8 bits.

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Longer Numbers Since 255 is the largest number that can be represented in 8 bits, lager values simply require longer numbers. For example, 27916 is represented by: 0011011010000110
Longer Numbers Since 255 is the largest number that can be represented in 8 bits, lager values simply require longer numbers. For example, 27916 is represented by: 0011011010000110 Can you remember the Binary representation?

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Short Forms for Binary Because large numbers require long strings of Binary digits, short forms have been developed to help deal with them. An early system used was called Octal. It’s based on the 8 patterns in 3 bits.
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Chapter_2(S) - BinaryNumberSystems PositionalNotation 104...

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