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Memory, Bits, Bytes, and BCD. Memory. Part of the computer where programs and data are stored. Read and written (changed). Bit Binary digit Basic unit of memory 1 or 0 Why binary? Because we can most reliably (electronically) distinguish between 1 and 0. Byte = 8 bits

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Memory
Memory

  • Part of the computer where programs and data are stored.

  • Read and written (changed).

  • Bit

    • Binary digit

    • Basic unit of memory

    • 1 or 0

    • Why binary? Because we can most reliably (electronically) distinguish between 1 and 0.

  • Byte = 8 bits

    • Smallest unit of memory that can be read or written.


Representing numbers
Representing numbers

  • Integers

    • 2’s complement is most popular

  • Real numbers

    • Floating point

      • IEEE 754 standard format is most popular

    • Fixed point

      • 2’s complement integers (using standard integer arithmetic)

      • BCD = binary coded decimal

  • All of the above are supported by IA32!


Bcd binary coded decimal
BCD = binary coded decimal

4 bit encoding of 0..9 (decimal)

base 10 base 2 BCD

0 0000 0000 same

1 0000 0001 "

2 0000 0010 "

3 0000 0011 "

4 0000 0100 "

5 0000 0101 "

6 0000 0110 "

7 0000 0111 "

8 0000 1000 "

9 0000 1001 "

10 0000 1010 0001 0000

11 0000 1011 0001 0001

12 0000 1100 0001 0010

. . .

? ? ?


Bcd binary coded decimal1
BCD = binary coded decimal

4 bit encoding of 0..9 (decimal)

base 10 base 2 BCD

0 0000 0000 same

1 0000 0001 "

2 0000 0010 "

3 0000 0011 "

4 0000 0100 "

5 0000 0101 "

6 0000 0110 "

7 0000 0111 "

8 0000 1000 "

9 0000 1001 "

10 0000 1010 0001 0000

11 0000 1011 0001 0001

12 0000 1100 0001 0010

… … …

99 0110 0011 1001 1001

100 0110 0100 invalid

… … invalid

255 1111 1111 invalid


Why bcd
Why BCD?

  • What happened when we converted 0.10 (base 10) to base 2?

    0.10 x 2 = 0.20 .0

    0.20 x 2 = 0.40 0

    0.40 x 2 = 0.80 0

    0.80 x 2 = 0.60 1

    0.60 x 2 = 0.20 1

    .

    .

    .



Memory addresses
Memory addresses

  • Each individually addressable “cell” is an 8-bit byte containing 28 = 256 possible values (0..255).

  • The number of memory cells is independent of the cell size.

  • Most modern processors have at least a 32-bit address space.

    232 = 4G bytes arranged 0..232-1


Integers in memory
Integers in memory

  • Each individually addressable “cell” is an 8-bit byte containing 28 = 256 possible values (0..255).

  • To allow for larger values, we group bytes together.

    • byte = 8 bits

    • word = 16 bits

    • double word = 32 bits (long word)

    • quadword = 64 bits


Byte ordering
Byte ordering

  • Consider a word consisting of 2 bytes in memory with a value of 080116 at address 10.

  • It is a word (2 bytes) so it occupies memory location 10 and memory location 11.

  • It can be stored in memory as either:

    M[10] M[11]

    08 01 - big endian (Motorola)

    01 08 - little endian (IA32, VAX)

    - either (switchable): IA64, ultraSparc


Endian ness
Endian-ness

  • Extends from 4 to 8 (and 16) byte integers too.

  • (Note: For integers larger than 2 bytes, other orderings are possible but they are not used.)


Endian ness conversion
Endian-ness conversion

  • big endian: Motorola

  • little endian: IA32, VAX

  • bi-endian: IA64, ultraSparc

    • either/both supported

    • typically switchable at boot time


Endian ness conversion1
Endian-ness conversion

  • What happens if one sends a message (that contains multi-byte integers) from one system to another across the internet, and they have different endian-ness?

    • We need a way to convert from one format to another (future topic; also see htonl Unix/Linux function).


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