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Memory, Bits, Bytes, and BCDPowerPoint Presentation

Memory, Bits, Bytes, and BCD

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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

- 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

- Floating point
- All of the above are supported by IA32!

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 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?

- 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

.

.

.

Binary and BCD addition

Add 9 + 1.

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

- 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

- 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

- 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

- big endian: Motorola
- little endian: IA32, VAX
- bi-endian: IA64, ultraSparc
- either/both supported
- typically switchable at boot time

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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