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Scaling
SCALING means to change the magnitude of a number. Shifting binary numbers to the left increases
their value, and shifting to the right decreases their value. The increase or decrease in value is based on
powers of 2.
A shift of one place to the left increases the value by a power of 2, which in effect is multiplying the
number by 2. To demonstrate this, let’s assume that the following block diagram is a 5-bit shift register
containing the binary number 01100.
0
1
1
0
0
Shifting the entire number one place to the left will put the register in the following condition:
1
1
0
0
0
The binary number 01100 has a decimal equivalent of 12. If we convert 110002 to decimal, we find it
has a value of 2410. By shifting the number one place to the left, we have multiplied it by 2. A shift of two
places to the left would be the equivalent of multiplying the number by 22, or 4; three places by 23, or 8;
and so forth.
Shifting a binary number to the right decreases the value of the number by a power of 2 for each
place. Let’s look at the same 5-bit register containing 011002 and shift the number to the right.
0
1
1
0
0
A shift of one place to the right will result in the register being in the following condition:
0
0
1
1
0
By comparing decimal equivalents you can see that we have decreased the value from 1210 to 610.
We have effectively divided the number by 2. A shift of two places to the right is the equivalent of
dividing the number by 22, or 4; three places by 23; or 8; and so forth.
