Binary Storage, Registers, ASCII Character Code, Gray Code

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Registers:

  • A register is a group of binary cells.  Each cell stores one bit of information. The state of a register is an n—tuple of 1’s and 0’s, with each bit designating the state of one cell in the register.
  • The content of a register is a function of the interpretation given to the information stored in it. See page 25.

Binary Logic:

  • Deals with variables that take on two discrete values and with operations that assume logical meaning.
  • The 2 values may be called by different names (e.g. true/false, yes/no, 0/1)
  • It is suited for the analysis and design of digital systems.

ASCII Character Code:

  • The standard binary code for representation of alphanumeric characters is ASCII (American Standard Code for Information Interchange). It uses 7 bits to code 128 characters.

Gray Code:

  • Gray code is used to represent the digital data when it is converted from analog data.
  • The advantage of the Gray code over binary numbers is that only one bit in the code group changes when going from one number to the next.
  • In Gray to go from:    7 to 8: 0100 -> 1100
  • In Binary to from:      7 to 8: 0111 -> 1000

Binary Codes:

  • Binary codes play an important role in digital computers. A bit is a binary digit. It is equal to 0 or 1.
  • Although the minimum number of bits required to code 2n quantities is n, there is no maximum number of bits that may be used for a binary code.

Signed Binary Numbers:

  • It is customary to represent the sign with a bit placed in the leftmost position of the number and to make it 0 for positive and 1 for negative.
  • Consider the number 9 represented in binary with 8 bits. +9 is represented with sign bit 0 in the leftmost position followed by the binary equivalent of 9 to give 00001001.

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