Encyclopedia of Computer Science and Technology

itwise operations 51in terms of bytes. A byte is 8 bits or binary digits, whichamounts to a range of from 0 to 255 in terms of decimal (base10) numbers. A byte is thus enough to store a small integeror a character code in the standard ASCII character set(see character). Common multiples of a byte are a kilobyte(thousand bytes), megabyte (million bytes), gigabyte (billionbytes), and occasionally terabyte (trillion bytes). The actualnumbers represented by these designations are actually somewhatlarger, as indicated in the accompanying table.Further Reading“How Bits and Bytes work.” Available online. URL: http://www.howstuffworks.com/bytes.htm. Accessed April 22, 2007.One byte in memory can store an 8-bit binary number. Just as eachplace to the left in a decimal number represents the next higherpower of 10, the places in the byte increase as powers of 2. Here theplaces with 1 in them add up to a total decimal value of 213.With regard to computer architectures the numberof bits is particularly relevant to three areas: (1) The sizeof the basic “chunk” of data or instructions that can befetched, processed, or stored by the central processing unit(CPU); (2) The “width” of the data bus over which data issent between the CPU and other devices—given the sameprocessor speed, a 32-bit bus can transfer twice as muchdata in a given time as a 16-bit bus; and (3) The width of theaddress bus (now generally 32 bits), which determines howmany memory locations can be addressed, and thus themaximum amount of directly usable RAM.The first PCs used 8-bit or 16-bit processors, whiletoday’s PC processors and operating systems often use 32-bits at a time, with 64-bit processors now entering the market.Besides the “width” of data transfer, the number of bitscan also be used to specify the range of available values.For example, the range of colors that can be displayed bya video card is often expressed as 16 bit (65,536 colors) or32 bit (16,777,777,216 colors, because only 24 of the bits areused for color information).Since multiple bits are often needed to specify meaningfulinformation, memory or storage capacity is often expressedbitwise operationsSince each bit of a number (see bits and bytes) can holda truth value (1 = true, 0 = false), it is possible to use individualbits to specify particular conditions in a system, andto compare individual pairs of bits using special operatorsthat are available in many programming languages.Bitwise operators consist of logical operators and shiftoperators. The logical operators, like Boolean operators ingeneral (see Boolean operators), perform logical comparisons.However, as the name suggests, bitwise logical operatorsdo a bit-for-bit comparison rather than comparing theoverall value of the bytes. They compare the correspondingbits in two bytes (called source bits) and write result bitsbased on the type of comparison.The AND operator compares corresponding bits andsets the bit in the result to one if both are one. Otherwise, itsets it to zero.Example: 10110010 AND 10101011 = 10100010The OR operator compares corresponding bits and setsthe bit in the result to one if either or both of the bits areones.Example: 10110110 OR 10010011 = 10110111The XOR (“exclusive OR”) operator works like ORexcept that it sets the result bit to one only if either (notboth) of the source bits are ones.Example: 10110110 XOR 10010011 = 00100101The COMPLEMENT operator switches all the bits totheir opposites (ones for zeroes and zeroes for ones).Example: COMPLEMENT 11100101 = 00011010Measurement Number of Bytes examples of Usebyte 1 small integer, characterkilobyte 2 10 1,024 RAM (PCs in the 1980s)megabyte 2 20 1,048,576 hard drive (PCs to mid-1990s)RAM (modern PCs)gigabyte 2 30 1,073,741,824 hard drive (modern PCs)RAM (latest PCs)terabyte 2 40 1,099,511,627,776 large drive arrays