BINARY SHIFT Multiplication and Division

Binary Shift  As you know a computer can only add, not subtract. For the same token it can still only add, not multiply or divide.  Multiplication is usually achieved by repeatedly adding, and division is usually achieved by repeatedly 'subtracting' (or as we know, adding through the use of two's complement).

Binary Shift  There are occasions when you can 'cheat' in multiplication/division, but only when the number you are multiplying/dividing by is a number on the binary scale eg. 2, 4, 8 etc. We'll stick with whole numbers

Binary Shift  Firstly, you need to remember the binary scale  Now you need to pay close attention to two things:  the number in each column  The exponent above the 2, that corresponds to each number  Eg. The number 8 has the exponent

Binary Shift: Left Shift  Now lets use a multiplication example:  5 x 8  We can start by determining the exponent that corresponds to 8, and re-write the question  5 x 2 3

Binary Shift: Left Shift  Remember the problem is: 5 x 2 3  Now use your columns to write down 5 in binary  Below you original value of 5, move all the bits 3 places to the left, and pad the holes with 0’s

Binary Shift: Left Shift  5 x 2 3 (or if you prefer 5 x 8) is equal to 40, this can be easily achieved by shifting the whole number 3 places up the binary scale.  Try the following two multiplications:  7 x 4  3 x 16

Binary Shift: Right Shift  Now lets look at a division example:  35 / 16  We can start by determining the exponent that corresponds to 16, and re-write the question  35 / 2 4

Binary Shift: Right Shift  Remember the problem is: 35 / 2 4  Now use your columns to write down 35 in binary  Below you original value of 35, move all the bits 4 places to the right

Binary Shift: Right Shift  35 x 2 4 (or if you prefer 35 / 16) is equal to , this can be easily achieved by shifting the whole number 4 places down the binary scale.  Try the following two divisions:  17 / 4  131 / 32

Binary Shift  At this point you should know that:  Multiplying is a Left Shift (because you are making the number bigger)  Dividing is a Right Shift (because you are making the number smaller)  If one of the numbers in the multiplication/division is a number on the binary scale, check the exponent of that number and move the other number up/down the scale by the number of places in the exponent