University:
Kentucky State University
Course:
COS 232 | Programming I
Academic year:

2023
Views:

294

Pages:

8
Author:

palangresq3v

Binary & Decimal Systems Bits & Bytes • Bits are binary digits; they are either 0s or 1s. • Bit (b) Binary digit, a 1 or 0 • Computers operate with electronic switches that are either "on" or "off", corresponding to 1 or 0. • A byte is a group of eight bits • Byte (B) 8 bits Decimal System Since we use only 10 digits in our daily calculations, our system of representing numbers is called “Decimal System”. So the numerical value Eight thousands nine hundred ﬁfty four is represented as: 8 9 5 4 = 8*103 + 9*102 + 5*101 + 4*100 Decimal number system • Base 10 because it uses ten symbols • 0,1,2,3,4,5,6,7,8,9 • 2134 could also be written as: (2x103) + (1x102) + (3x101) + (4x100) Binary System Since a computer is a machine that can only work on two states: “ON” or “OFF” or two electrical pulse states “High” or “Low”, or two logical states “True” or “False” or simply 1 or 0 So the alphabet in computers is only formed of two entities (rather than 10 in the decimal system). That is why it is called “Binary System”. Binary number system • Base 2 because it uses 2 symbols • 0&1 • Computers recognize and process data using the binary (Base 2) numbering system • The position, or place, of each digit represents the number 2 – the base number – raised to a power (exponent), based on its position (20, 21, 22, etc.) 10110 = (1 x 24 = 16) + (0 x 23 = 0) + (1 x 22 =4) + (1 x 21 = 2) + (0 x 20 = 0) = 22 Binary System Numerical Values in Binary System are represented as a combination of 1’s and 0’s, For example Decimal Binary 0 0 1 1 2 10 3 11 4 100 . . 8 1000 9 1001 etc.. Binary System Notice the Following: Decimal Binary 3 = 3*100 11 = 1*21 + 1*20 10 = 1*101 + 0*100 1010 = 1*23+0*22+1*21+0*20 So what is the decimal value of this binary number: 1 0 0 1 0 1 ?