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Memory, Bits, Bytes, and BCD

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, Bits, Bytes, and BCD

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  1. Memory, Bits, Bytes, and BCD

  2. 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.

  3. 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!

  4. 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 . . . ? ? ?

  5. 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

  6. 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 . . .

  7. Binary and BCD addition Add 9 + 1.

  8. 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

  9. 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

  10. 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

  11. 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.)

  12. Endian-ness conversion • big endian: Motorola • little endian: IA32, VAX • bi-endian: IA64, ultraSparc • either/both supported • typically switchable at boot time

  13. 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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