# Language of Computers – Binary

The digital computer is a digital system that performs various computational tasks.

Generally the word digital means:

- recording or
**showing information in the form of numbers**, esp. 0 and 1 **showing information as whole numbers**rather than in another form such as a picture, graph, etc.- of relating to, or using calculation by numerical methods or by discrete units (different, unique, and separate units).

Here the word digital implies a system that can be used by a computer and other electronic equipment, in which **information is sent and received in electronic form as a series of the numbers 1 and 0**

The first electronic digital computers, developed in the late 1940s, were used primarily for numerical computations. In this case, the discrete elements are the digits (ie., 0, 1,2…9). From this application, the term digital computer has emerged.

In practice, digital computers function more reliably if only two values are used.

### Why?

**Computers don’t understand **words or numbers the way we humans do. In the end, everything in the computer is represented by a binary electrical signal that registers data in one of two states: ON or OFF

Any instructions you give to the computer gets converted to binary. Later gets stored, processed within the system. Output again will be presented in the format we humans can understand.

This ON or OFF usaually represented with two numbers 0 and 1.

Digital computers use the binary number system, which has two digits: 0 and 1. A binary digit is called a bit.

In digital computers, information is represented in groups of bits.

- A group of eight bits is called a byte.
- Most computer memories use words whose number of bits is a multiple of 8.
- Thus a 16-bit word contains two bytes, and
- a 32-bit word is made up of four bytes.

It is customary to refer to the number of words (or bytes) in a memory with one of the letters

**1 KB** (kilobyte) is 2^{10} = **1024 bytes**,

**1 MB** (megabyte) is 2^{20} = **1024 Kilo bytes**,

**1 GB** (gigabyte) is 2^{30} = **1024 Mega bytes**, etc.,

By judicious use of binary arrangements and by using various coding techniques, the groups of bits are used to develop complete sets of instructions for performing various types of computations.

In contrast to the common decimal numbers that employ the base 10 system, binary numbers use a base 2 system with two digits: 0 and 1.

The decimal equivalent of a binary number can be found by expanding it into a power series with a base of 2.

For example, the binary number **1001011 **represents a quantity that can be **converted to a decimal number by multiplying each bit by the base 2 raised to an integer power** as follows:

binary base positions | 2^{6}=64 | 2^{5}=32 | 2^{4}=16 | 2^{3}=8 | 2^{2}=4 | 2^{1}=2 | 2^{0}=1 |

given binary number | 1 | 0 | 0 | 1 | 0 | 1 | 1 |

multiply base positions with the respective binary digit | 1×64=64 | 0x32=0 | 0x16=0 | 1×8=8 | 0x4=0 | 1×2=2 | 1×1 =1 |

**Total sum is 64+0=0+8+0+2+1 = 75**

However, **this same group of seven bits represents the letter K** when used in conjunction with a binary code for the letters of the alphabet.

It may also represent a control code for specifying some decision logic in a particular digital computer.

In other words, groups of bits in a digital computer are used to represent many different things.

Similarly, first few decimal equivalent for binary is given below.

Decimal number | Binary number |
---|---|

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

**Next**:

Memory and binary data