Intro to Computer Science Chapter 2

number

unit of an abstract mathematical system subject to the laws of arithmetic

natural number

number 0 and any number obtained by repeatedly adding 1

negative number

value less than 0 with a sign opposite to positive counterpart

integer

a natural number, a negative of a natural number, or zero

rational number

integer or the quotient of two integers (division by 0 excluded)

base

specifies number of digits in a system and the value of digit positions

positional notation

system of expressing numbers in which the digits are arranged in succession, the position of each digit has a place value, and the number is equal to the sum of the products of each digit by its place value

converting to base 10

raise the base number (base 13, 10,2, etc.) to the position value, then multiply by the digit in that position. Add all the values together. 943 (base 13) = 1576 (base 10)

binary

base-2 (0,1)

octal

base-8 (0,1,2,3,4,5,6,7)

hexadecimal

base-16 (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)

power of 2 relationships

754 in octal is 111101100 in binary by replacing each separate octal number with the equivalent binary number 111-101-100. From binary to octal, group in 3's from right to left, and convert to octal digit. Same for binary-hexadecimal, except in groups of four

converting from base 10

Divide number by new base. The remainder is the new digit added to the left of final answer. Replace decimal number with quotient. Repeat until quotient is 0.

modern computers

represented in binary values, where each storage location has either a low or high voltage signal

binary digit

digit in the binary number system (0 or 1)

bit

short for binary digit

byte

8 binary digits (bits)

word

group of 1 or more bytes number of bits in a word = word length of the computer