Advanced Binary for Programming & Computer Science

This book explains how the binary works & how it is used by computers to represent information including positive & negative integers, characters & real numbers. It explains the logical & bitwise operations used to manipulate information & perform arithmetic. We also briefly look at how computers store this information in memory & secondary storage, & how it can be transmitted between computers.

Topics covered include:

INTRODUCING NUMBER BASES & BINARY

CONVERTING FROM BINARY TO DENARY & VICE-VERSA
How to Convert a Binary Number to Denary
How to Convert a Denary Number to Binary

HOW COMPUTERS GROUP BINARY DIGITS
A Closer Look at Bytes
A Closer Look at Words
-Word alignment, word alignment & packing, byte ordering & endianness
Addresses

BOOLEAN OPERATIONS & LOGIC GATES
Fundamentals of Boolean Algebra
-NOT, AND, OR, XOR, NAND, NOR, NXOR
Combining Logic Gates
-NOT, AND, OR, XOR, NOR using NAND logic
Logical Versus Bitwise Operations
Using Bitwise Operations to Set, Clear, Flip or Test Bits
-Setting bits, inverting bits, clearing bits, testing bits

ADDING & SUBTRACTING IN BINARY
Adding Binary Integers
-The column addition method of adding denary numbers & adding binary numbers, implementing binary addition using logic gates
Subtracting Binary Integers
-The column subtraction methods of subtracting denary numbers & subtracting binary numbers, implementing binary subtraction using logic gates

SHIFT OPERATIONS
Left Shift
Right Shift
Circular Shifts

MULTIPLICATION & DIVISION IN BINARY
Multiplication
-Multiplying by a power of 2, column multiplication, Russian peasant multiplication algorithm, multiplication in hardware
Division
-Dividing by a power of 2, denary long division, binary long division, algorithm for binary long division, division in hardware

REPRESENTING CHARACTERS & STRINGS OF CHARACTERS
Representing Individual Characters
-ASCII, extended ASCIIs, BCDIC & other early character encodings, EBCDIC, Unicode
Representing Strings of Characters
-Terminated strings, length-prefixed strings, other string representations

REPRESENTING TEXT & GRAPHICS ON SCREEN
Text Mode Displays
Bitmap Displays

PARITY CHECKING
What is a Parity Bit
Even & Odd Parity
Advantages, Disadvantages & Limitations of Using Parity Checking
Parity's Use in RAID Storage Devices
Unused Parity Bits

SIGNED INTEGERS
Offset Binary
Signed Magnitude Representation
One's Complement
Two's Complement
Other Representations of Signed Numbers
-Base -2, signed-digit representation

REAL NUMBERS
Fixed Point Representation
Floating Point Representation
Rational Data Type
Logarithmic Number Systems

DENARY ENCODINGS & DECIMAL DATA TYPES
Why Use Denary Representations of Real Numbers?
Binary Encodings of Denary
-Serial decimal, two-out-of-five, bi-quinary, character...