Nguyen Le CS147

 2.4 Signed Integer Representation  – Signed Magnitude  – Complement Systems  – Unsigned Versus Signed Numbers  – Computers, Arithmetic, and Booth’s Algorithm  – Carry Versus Overflow Section overview

Unsigned integer representation   carries   

3 methods of representation  Signed magnitude  One’s complement   Two’s complement

Signed magnitude  Signed magnitude representation includes a sign as the first bit of the storage location. A “1” in the high-order bit (or left- most bit) indicates a negative number and the rest of the remaining bits represent the number itself. Ex: +1 and -1 in an 8-bit word would be  (+1)  (-1)

Signed magnitude addition   carries   

Overflow  Overflow in signed numbers occurs when the sign of the result is incorrect. The sign bit is used only for the sign, so we can’t carry into it.   carries  (79)  (99)  (50) =/= 50

Signed magnitude subtraction   borrows  (99)  (79)  (20)   99 – 79 = 20

One’s compliment  1   carries  (23)  (-9)   + 1  (14) Flip the bits for all negative numbers. The last carry is added to the sum.

Two’s compliment  (9)  (-23)  (-14) Flip the bits for all negative numbers. Add = = =

 2.6Character Codes  – Binary-Coded Decimal  – EBCDIC  – ASCII  – Unicode Section overview

Character codes  We’ve gone over how digital computers use the binary system to represent and manipulate numeric values, but have yet to consider how these internal values can be converted to a form that is meaningful to humans. This is done through a coding system used by the computer and how the values are stored and retrieved.

BCD  Binary Coded Decimal (BCD) is very common in electronics, particularly those that display numerical data, such as alarm clocks and calculators.  4-bit binary form later extended to 6  1265 =

EBCDIC  Extended Binary Coded Decimal Interchange Code (EBCDIC) used in IBM mainframe and midrange computer systems  8-bit binary form  1265 =

ASCII  The American Standard Code for Information Interchange (ASCII) was created to better transmit data between systems.  Defines codes for 32 control characters, 10 digits, 52 letters (upper and lower- case), 32 special characters, and more.

Unicode  16-bit base coding with the capacity to encode the majority of characters used in every language of the world.  Unicode also defines an extension mechanism that will allow for the coding of an additional million characters.  Default character set of the Java programming language.