Number Systems - Coursework Example

In this system, 0 is called as the Least Significant Bit (LSB) while 1 is called the Most Significant Bit (MSB). Binary system is the computer language by default because 0 and 1 in computer signify voltage positions of on and off. Hexadecimal system uses base-sixteen system for computing. It has 16 digits but since numbers are only from 0-9, letters are also termed as valid hexadecimal digits (Ratzan 18). As such, letters from A to F are included in hexadecimal system after counting 0-9 where A stands for 10, B for 11 and so on.

In this system, one digit is equivalent to 4 bits. Inter-relationship of these three systems is depicted in Appendix 1. When converting from decimal to hexadecimal, the same rule of successive divisions is followed as mentioned above. When reverse is done, same power raising method is used but now with 16 as the base and place values as exponents. In this conversion, the binary digit is grouped in blocks of four, starting from right hand. Additional zeroes are added to the left to complete the grouping.

After grouping is completed, corresponding hex digit for binary blocks is noted down from the conversion table. For example, (0010101001)2 comprises of 10 bits. Thus we have to add two additional zeroes to its left to complete blocks of 4. Addition and subtraction of 2’s complement is actually always addition, just the subtrahends are converted to their negative forms when carrying out subtraction. In binary form, leftmost digit 1 represents a negative number while leftmost digit 0 represents a positive number.

Let’s have a look at the addition and subtraction of 2’s complement (Finley