SHREE BALAJI CLASSES

Complement of a Number    Octal and Hexadecimal Number    Convert Decimal to Binary Subtraction of numbers by using complement Subtraction with r’s Complements The direct method of subtraction taught in elementary schools uses the borrow concept. In this method, we borrow a 1 from a higher significant position when the minuend digit is smaller than the corresponding subtrahend digit. This seems to be easiest when people perform subtraction with paper and pencil. When subtraction is implemented by means of digital components, this method is found to be less efficient than the method that uses complements and addition as stated below.      The subtraction of two positive numbers (M - N), both of base r, may be done as follows: 1.        Add the minuend M to r’s complement of the subtrahend N. 2.        Inspect the result obtained in step 1 for an end carry: a.        If the end carry occurs, discard it. b.       If an end carry does not occur, take r’s complement of

     This article is used to find out the square of  a number in a short period of time compare to normal maths. It increase the speed of your calculations.  The answer obtained by multiplying a number by itself is the square of that number. Example :- 6×6= 36 which is the square of 6.                          8×8= 64 which is the square of 8.      1.   Square of numbers ending in 5 :- Example 1-: 35 2 =   ? Step 1:- Multiply the first part by the first part plus 1: 3 ×(3+1) =3×4 =12 Step 2:- Write the number 25 next to the result from step 1: 35 2 = 12_25 = 1225 Example 2-: (in 3 digits) 125 2 =   ? Step 1:- Multiply the first part by the first part plus 1: 12 ×(12+1) =12×13 =156 Step 2:- Write the number 25 next to the result from step 1: 125 2 = 156_25 = 15625 Example 3-: (in decimal numbers) 9.5 2 =     ? Step 1:- Multiply the first part by the first part plus 1: 9 ×(9+1) =9×10 =90 Step 2:- Write the number 25 next to the result from step

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 complement of (25.639)10 is