Chapter 1 Final Revision #1

Base two number system based on the values 0 and 1.

A Bit is the abbreviation for binary digit. It is the smallest unit of digital information. The system is ideal because it uses digits 0 and 1, corresponding to the simple ON/OFF switch mechanism that logic gates opperate by.

4 bits are referred to as a Nibble. 8 bits are referred to as a Byte.

A base 16 number system, which uses the denary digits 0 to 9 and the letters A to F.

• It is easier to represent and manage compared to long binary sequences. • It is used in Memory Dumps and during program debugging.

Contents of computer memory output to a screen or printer.

A character set is a list of all of the characters that can be used/represented by the computer hardware and software. Each character has a unique binary number. To convert a string: each character is replaced by its binary value and stored in sequence as its binary value, using the character set.

ASCII is a character set for all characters on an English keyboard and control codes. It uses 7 bits, allowing for 128 different codes/characters.

Extended ASCII uses 8 bits, allowing for 256 different codes/characters.

Unicode is a character set which represents all languages of the world. It commonly uses 16 bits per character, and can use up to 4 bytes (32 bits) per character, which means that it can represent up to 2^32 unique characters.

The first 128 characters of Unicode are the same as ASCII.

• Unicode has greater range of characters than ASCII • Unicode represents most written languages in the world while ASCII does not • ASCII used for English only • ASCII uses 7 or 8 bits or one byte whereas Unicode uses up to 4 bytes per character (commonly 16 bits)

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

Successive addition. Each ‘1’ in a column adds the column value (weighting) to the total. Example: 01101011 = 64 + 32 + 8 + 2 + 1 = 107 (in Denary).

Successive subtraction. By subtracting the binary weightings, largest (possible) to smallest, from the number unti we reach 0 and writing 1s in those columns. Example: To convert 58: 58- 32-16-8-2=0, resulting in binary: 00111010. [If the number is odd, the rightmost bit is 1]

The left-most bit (MSB) is used to represent the sign (0= positive, 1= negative); the remaining bits represent the binary value.

Each binary digit in a number is reversed (flipped) to allow both negative and positive numbers to be represented.

Two’s Complement is the one’s complement of a binary number plus 1 to the rightmost bit. It is used to represent negative numbers, and the most significant bit carries the negative of the equivalent value.

• Take positive denary number (13) and convert to binary (00001101). • Flip each bit (One’s Complement): 11110010. • Add 1 to the One’s Complement. Result: 11110011 is -13 in denary.

Convert the second number (the subtrahend) into its 2’s complement, and then add the two numbers together. [Both numbers must be in two’s complement, don’t include overflow bits in the final answer].

103 + (-50). 103 is 01100111. 2’s complement of 50 is 11001110. Adding them gives 00110101 (53 in Denary). [Both numbers must be in two’s complement, don’t include overflow bits in the final answer]

It occurs when adding two large positive numbers in two’s complement which results in a number that is too large to be represented in the given number of bits. The result is erroneously represented as a negative number.