BINARY AND HEXADECIMAL NUMBERS

BINARY NUMBERS

The binary number system, or base-two, is a counting technique that uses two digits: 0 and 1. Here, the prefix 'bi' means 'two.'

The following are the applications of binary numbers.

1.      Representing images on screen. The images on the screen are from combinations of pixels which is the result of digital encoding represented with 1 and 0.

2.      Boolean algebra concept.   Boolean algebra numbers are represented in one and zeros which is in binary to solve binary logical equations using the truth values.

3.      Computer flips switches.    Numbers can be encoded in binary format and stored using switches. The digital technology which uses this system could be a computer, calculator, digital TV decoder box, cell phone etc. Values are stored in binary format in memory, which is basically a bunch of electronic on/off switches.

4.      Binary adder.   It adds two binary numbers and yields a binary result. It basically produces the sum of two numbers (A and B) and takes care of the carry (if any).

5.      Binary multiplier.   The primary design of a multiplier consists basically of adders only. Using long multiplication, a product of two N-bit numbers can be expressed as the sum of N N-bit partial products, which are then added to produce a 2N-bit product. The partial products can be computed from the fact that ai – bj = ai AND bj. The complexity of the multiplier is in adding the partial products.

6.      Digital binary clock.  A Digital Binary Clock consists of LEDs arranged separately for Hours, Minutes and Seconds as shown below- A LED in ON (lighted) state symbolizes a Binary 1 and on the contrary a LED in OFF state symbolizes a Binary 0.

HEXADECIMAL

It describes a base-16 number system. That is a numbering system containing 16 sequential numbers as base units (including 0) before adding a new position for the next number. The following are the applications.

• To define locations in memory. Hexadecimals can characterize every byte as two hexadecimal digits only compared to eight digits when using binary.
• To define colors on web pages. Each primary color – red, green and blue is characterized by two hexadecimal digits.  The format being used is #RRGGBB.  RR stands for red, GG stands for green and BB stands for blue.
• To represent Media Access Control (MAC) addresses. MAC addresses consist of 12-digit hexadecimal numbers.  The format being used is either MM:MM:MM:SS:SS:SS or MMMM-MMSS-SSSS.  The first 6 digits of the MAC address represent the ID of the adapter manufacturer while the last 6 digits represent the serial number of the adapter.
• To display error messages. Hexadecimals are used to define the memory location of the error.  This is useful for programmers in finding and fixing errors.

Hexadecimal numbers are of very high importance in your carreers basically IT.

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