summary
● The binary number system is the simplest number system.
● The binary number system contains two digits, 0 and 1.
● The binary number system is used to represent data for digital and computer systems.
● Binary data are represented by binary digits called bits.
● The term bit is derived from binary digit.
● The place value of each higher digit’s position in a binary number is increased by a power of 2.
● The largest value that can be represented by a given number of places in base 2 is 2n 21, where n represents the number of bits.
● The value of a binary digit can be determined by adding the product of each digit and its place value.
● Fractional numbers are represented by negative powers of 2.
● To convert from a decimal number to a binary num- ber, divide the decimal number by 2, writing down the remainder after each division. The remainders, taken in reverse order, form the binary number.
● Octal numbers allow reading large binary numbers by breaking the binary number into groups of three.
● The octal number system is referred to as base 8.
● Similar steps are used to convert octal numbers to decimal and decimal numbers to octal as with the binary number system.
● The hexadecimal number system breaks binary numbers into groups of four to reduce error when entering data.
● The hexadecimal number system is a base-16 system.
● The hexadecimal number system is used with microprocessor-based systems.
● As with octal and binary number systems, the hexadecimal number system uses similar steps for converting to and from decimal numbers.
● The 8421 code, a binary-coded decimal (BCD) code, is used to represent digits 0 through 9.
● The advantage of the BCD code is ease of convert- ing between decimal and binary forms of a number.
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