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Complement of a Number

Subtraction of Binary Numbers  ;  Octal and Hexadecimal Number  ;  Convert Decimal to Binary Complements Complements are used in digital computers for simplifying the subtraction operation and for logical manipulations. There are two types of complements for each base-r system: (1) the r’s complement and (2) the (r-1)’s complement. When the value of the base is substituted, the two types receive the names 2’s and 1’s complement for binary numbers,  10’s and 9’s complement for decimal numbers. The r’s Complement Given a positive number N in base r with an integer part of n digits, the r’s complement of N is defined as r n   - N for N is not equal to 0 and 0 for N = 0. The following numerical example will help clarify the definition. The 10’s complement of (52520) 10 is 10 5 – 52520 = 47480 The number of digits in the number is n= 5 The 10’s complement of (0.3267) 10 is 1 – 0.3267 = 0.6733 No integer part, so 10 n = 10 0 = 1 The 10’s...
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mathematics skills

Are you ready to give your mathematics skills a boost? These simple math tricks can help you perform calculations more quickly and easily. They also come in handy if you want to impress your teacher, parents, or friends. 01 The Answer Is 2 Think of a number. Multiply it by 3. Add 6. Divide this number by 3. Subtract the number from Step 1 from the answer in Step 4. The answer is 2. Same Three-Digit Number Think of any three-digit number in which each of the digits is the same. Examples include 333, 666, 777, and 999. Add up the digits. Divide  the three-digit number by the answer in Step 2. The answer is 37. Six Digits Become Three Take any three-digit number and write it twice to make a six-digit number. Examples include 371371 or 552552. Divide the number by 7. Divide it by 11. Divide it by 13. The order in which you do the division is unimportant! The answer is the three-digit number. Examples: 371371 gives you 371 or 552552 gives you 552. A related trick is to take any three-di...
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Types of Number System

Different Number Systems – There are some different Number System with correspondence base. Which will describe as follows-   Number System  Base  Representation  Binary Number System      2  (Number) 2  Decimal Number System      10  (Number) 10  Octal Number System      8  (Number) 8  Hexadecimal Number System     16   (Number) 16 Note : Any number can be in decimal form. So there is an another way to solve them quickly. Let’s understand with an example. Ex 1. (4064.10) 10   Sol. This Number can also be written as (4*10 3 ) + (0*10 2 ) + (6*10 1 ) + (4*10 0 ) + (1*10 -1 ) + (0*10 -2 ) Note that after decimal digits we will use decreasing power of 10 from left to right. Ex 2.   (1101.01) 2        Sol. This Number can also be written as (1*2 3 ) + (1*2 2 ) + (0*2 1 ) + (1*2 0 ) + (0*2 -1 ) + (0*2 -2 ) Exercise: From Ques...
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