Computer Data Representation

Word

A sequence of N bits. Where N varies from computer to computer. It is a unit of data. There are: 8-bit /1 bytes 16-bit/2 bytes 32-bit/4 bytes 64-bit/8 bytes etc

Nibble

A unit of data, it is 4 bits. It can be represented by a single hexadecimal digit and has 16 possible values. Divide by two and the latter half is high order the lower is low order.

Division method to convert from DECIMAL to HEXADECIMAL?

1. Divide by decimal value by 16 2. Continuously divide the quotient by 16 noting the remainder (will always be 0 - F) 3) Read list of remainders bottom to top to get answer from left to right in binary.

Division method to convert from DECIMAL to BINARY?

1. Divide by decimal value by 2 2. Continuously divide the quotient by 2 noting the remainder (will always be 0 or 1) 3) Read list of remainders bottom to top to get answer from left to right in binary.

The total combination of values that can be found in n bits is?

2ⁿ combinations. Not to be confused with the maximum value that can be held in n bits which is (2ⁿ - 1)

Decimal System?

A base 10 number system (0-9) Each column represents 10 times the previous

Octal System?

A base 8 number system (0-7) Each column represents 8 times the previous.

Radix

Another name for base

MSB and LSB

Most significant bit: Left-most bit Least significant bit: Right-most bit

How is binary addition performed?

Basically if a column has: Two 1's = 0 in the column and carry a 1 to the next Three 1's = 1 in the column and carry a 1 to the next

How is binary multiplication performed?

Basically the same as decimal.

Signed values

Can be negative or positive values. Since negative values are included the max range is halved in both directions. That is, signed values hold a smaller positive amount.

Number System

Multiple ways of representing the same value with numbers with different conventions.

How is the Two's Complement Computed?

Don't forget the negative sign if the ORIGINAL value began with a 1.

Byte

Eight binary digits. It represents 2⁸ (256) bit value combinations.

Convert from binary to octal or vice-versa?

Every 3 binary bits is an octal digit Every octal digit is 3 binary bits

Any number higher than 9 in HEXADECIMAL is represented by what?

Letters A(10) - F(15)

Unsigned Values

Positive only values

Word Length

Refers to: 8-bit, 16-bit, 32-bit, 64-bit machines Computers with longer word lengths are more powerful as they can process more chunks of data per unit.

Radix Point

The divider between whole number integer and fractional. Called: binary point in base 2 decimal point in base 10 octal point in base 8 hexadecimal point in base 16

Bit

A binary digit that represents off (0) or on (1).

Convert from binary to hexadecimal or vice-versa?

Similar to octal except you group the bits in 4s then convert them to hexadecimal digits.

Hexadecimal System?

A base 16 number system (0-F) Each column represents 16 times the previous.

How is binary subtraction performed?

When borrowing always carry over two 1's to subtract from.

All information stored on a computer boils down to ____

being stored as a representation of numbers: 0 and 1