* 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 2
^{n}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.