Arithmetic

2.0 ARITHMETIC FOR COMPUTER

A binary number operation will be focusing only in addition, subtraction, multiplication and division. The fundamental explorations on computer binary number operation will be more enjoyable if we have a basic understanding of the number calculation between the human and computer. Therefore, by computing basic types of number operation is superior practice in the following parts.

2.1 Binary addition

Binary Rules	Sum	Carry
0 + 0 = 0	0	0
0 + 1 = 1	1	0
1 + 0 = 1	1	0
1 + 1 = 1	0	1

How to add Binary numbers

Step 1 :

Align the numbers you wish to add as you would if you were adding decimal numbers.

Step 2 :

Start with the two numbers in the far right column

Step 3 :

Add the numbers following the rules of decimal addition (1+0 = 1, 0+0 = 0) unless both numbers are a 1.

Step 4 :

Add 1+1 as "10" if present. (it is not "ten" but "one zero"). Write "0" below and carry a "1" to the next column.

Step 5 :

Start on the next column to the left.

Step 6 :      

Repeat the steps above, but add any carry. Remember that 1+1 = 10 and 1+1+1 = 11. Remember to carry the "1".

TIPS:

<·         Dont forget to carry

<·       You can only use the digits 0 and 1. If you find yourself using 2 or any other digit, you did something wrong.

2.2 Binary Subtraction

Here are some examples of binary subtraction. These are computed without regard to the word size, hence there can be no sense of "overflow" or "underflow". Work the columns right to left subtracting in each column. If you must subtract a one from a zero, you need to “borrow” from the left, just as in decimal subtraction.

2.3  Multiplication

Multiplication in binary is similar to its decimal counterpart. Two numbers A and B can be multiplied by partial products: for each digit in B, the product of that digit in A is calculated and written on a new line, shifted leftward so that its rightmost digit lines up with the digit in B that was used. The sum of all these partial products gives the final result.

Since there are only two digits in binary, there are only two possible outcomes of each partial multiplication:

If the digit in B is 0, the partial product is also 0

If the digit in B is 1, the partial product is equal to A