Binary, Decimal and Hexadecimal
- 3. Introduction to Number systems Modern day computers use electricity to work. Inside the microchip electricity is turned either ON or OFF which is represented by 0’s and 1’s. This is called binary. Before we understand how a binary system works, You first need to know how our age-old numeric system work, i.e, the decimal system or the base 10 numeral system.
- 4. Decimal Number system There are 10 symbols that we use for counting our numbers they are 0,1,2,3,4,5,6,7,8,9. We then use this same symbol over and over again in a very clever system called the positional notation. As soon as we reach 10 or an exponent of 10 , we add another digit to the left of our current digit.
- 5. Base 10 representation of a number
- 6. Binary Number System What if we have only 2 numbers instead of 10 to work with? Binary works exact the same way as Base 10 numeral system. Base 10 Greater than 9 = New Digit Base 2 Greater than 1 = New Digit So, It goes like this 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 Since in Binary system each digit can have only 2 values. Each additional digit represents an increasing power of 2 rather than increasing power of 10
- 7. Base 2 representation of a number
- 8. Easy way of Converting decimal to binary A half byte is called a Nibble. i.e 4 Bits. With 4 bits we can use 16 different combinations of 0’s and 1’s. Since the decimal numbers are from 0- 9, 10 symbols in total , all of them can be represented in 4 bits. Write the value of exponent form of 2 from 2^0 - 2^3 in one row.For 1, in the column that has 2^0. Determine the power of 2 which sum upto the given digit, add 1’s to the one you have used and 0’s to the ones which you have not used. For example for 5, 4+1 makes 5, so write a 1 under 2^2 and 2^0 and 0 under 2^1 and 2^3, this make 0101. 8 4 2 1 0 0 0 0 0 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 2^3 2^2 2^1 2^0
- 9. Why Hexadecimal? In microprocessors and microcontrollers we deal with hexadecimal system. Everyone might wonder why we are ditching the good-old decimal system. There is a lot of explanation to it. By now, You are pretty clear about the decimal system and the conversion of decimal to binary. In the previous slide we found that with 4 bits, we can make upto 16 combinations of 0’s and 1’s. But with Base 10 system , we are restricted to 10 combinations and 6 more are going for a toss and then the concept of Base 16 system was created. 6 combinations , they don’t have an equivalent representation in binary. These 6 combinations from 10-15 are represented in hexadecimal as A-F.
- 10. Hexadecimal Advantage Every possible binary combination has now representation.On a single digit you are getting 16 values. That’s more information in less space. There came a need for a new system which represents 16 symbols, that is why base 16 system was created where 0-9 is represented as it is and from 10-15, is represented A-F. You may wonder why not just decimal, why hexadecimal. The highest four digit number if 9999, byt in hexa it if FFFF which is close to 50,000 more representation in form of data. Both are using the same space but more information is given only in hexadecimal system
- 11. Hexadecimal in Microcontrollers 1. In computers, we do not use the decimal system, It's only for the real world. 2. Inside the computer everything is in the form of binary, but it is not the binary form of decimal numbers but the binary form of hexadecimal numbers. So, that you can represent the combination of every 4 bits. So, let’s take some examples for easy conversion of Hexadecimal to binary 1. 35H 8 4 2 1 8 4 2 1 0 0 1 1 0 1 0 1 3 5
- 12. Try these.. For every digit you represent four bits. In microprocessor everything is represented in Hexadecimal, so each digit has to be converted to binary with 4 bits allocated for each digit. So, the numbers on the left require totally 8its. In uC we come across 8bit and 16bit numbers every time. So, what the range of an 8 bit number in hexadecimal 00 H -FF H. Which in decimal is -0-255 . Likewise for a 16 bit number is 0000 H - FFFF H , i.e. 0-65535 74 H 93 H FF H Find 8-bit or 16-Bit number 25 H 5140 H 809 H 245 H 30 H 5136 H
- 13. Powers of 2 Bits, Bytes and More 2^0 1 2^1 2 2^2 4 2^3 8 2^4 16 2^5 32 2^6 64 2^7 128 2^8 256 2^9 512 2^10 1024
- 14. 2^10 is 1024 and also called as 1KBytes. 2^20 = 2^10 * 2^10 = 1Kb * 1Kb = 1Mb 2^30 = 2^10 * 2^20 = 1Kb * 1Mb = 1Gb 2^40 = 2^20 * 2^20 = 1Mb * 1Mb = 1Tb So, when i say 4 Gb , what it means 2^2 * 2^30 = 2^32 Gb When said 2^36 it means 2^6 *2^30 = 64Gb 256Gb = 2^8*2^30 = 2^38 2^11 2Kb 2^12 4Kb 2^13 8Kb 2^14 16Kb 2^15 32Kb 2^16 64Kb 2^17 128Kb 2^18 256Kb 2^19 512Kb 2^20 1Mb 2^21 2Mb
- 15. Thank You