Chapter_2(S) - BinaryNumberSystems PositionalNotation 104...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
    Binary Number Systems
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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.
Background image of page 2
    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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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 .
Background image of page 4
    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.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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 .
Background image of page 6
    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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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
Background image of page 8
    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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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.
Background image of page 10
    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.
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
    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
Background image of page 12
    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?
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
  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.
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 54

Chapter_2(S) - BinaryNumberSystems PositionalNotation 104...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online