Bits, Bytes and Binary number system

Much like the decimal system, binary number system is used to represent numerical values using a combination of 0s and 1s. Analog systems use signals that are constantly changing in voltage or frequency. However, digital systems like computers, use signals containing just two voltage states namely logic ‘0’ and ‘1’. Use of the binary system makes it much easier to store and manipulate data. A simple switch or a transistor, which has two distinct states ‘on’ and ‘off’, can be used to store data, hence making computer design simple, efficient and cost effective.

The smallest unit of storage is called a bit. Bit stores one binary value of 0 or 1. A byte consists of 8 bits. Most computer storage space is measured in bytes. Every alphanumeric character of text can be written as a single byte using the most commonly used American Standard Code for Information Interchange(ASCII) encoding standard. Each numeral position in a binary number has a place value. In decimal numbers, each digit in a number has a place value which is represented as ones place, tens place, thousands place etc. Similarly, in binary numbers the place value is 2^0(1), 2^1(2), 2^2(4) etc.

Converting binary number to decimal

Let's take a binary number 1011. Starting from right to left, the decimal value is 1x2^0 + 1x2^1 + 0x2^2 + 1x2^3= 1 + 2 + 0 + 8 = 11
Let's look at another binary number 1100. The decimal value is 0x2^0 + 0x2^1 + 1x2^2 + 1x2^3 = 0+ 0 + 4 + 8 = 12
By using 4 bits in the binary number system, we can represent decimal numbers from 0 to 15 using the conversion method shown above.
0000--->0 1000--->8
0001--->1 1001--->9
0010--->2 1010--->10
0011--->3 1011--->11
0100--->4 1100--->12
0101--->5 1101--->13
0110--->6 1110--->14
0111--->7 1111--->15

Arithmetic operations such as addition, multiplication, subtraction etc, can be performed on binary numbers just like decimal numbers. The only rule to remember for addition and subtraction is to remember that each digit can have a 0 or 1 value, accordingly the carry or borrow from the next digit has to be taken. For example 10+11=101 (2+3=5). In multiplication, 1x1=1, 0x1= 0. In division, any digit divided by 0 is undefined.

Any file containing text, speech, video, audio or images can be digitized. Here digitize essentially means to turn the analog signal/data containing ranges of voltages to series of 0s and 1s. The process involves taking frequent samples of the data and converting them to numeral values. Numerical values can be easily translated as 0s and 1s which the digital device can process and store. For images, the whole image is split into pixels and numerical values are assigned according to the color at that position. This is also the reason why large picture files are clearer, as they store more number of pixels. Isn’t it amazing that so many things can be accomplished by just using 0s and 1s?

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