3-34ScalingSCALING means to change the magnitude of a number. Shifting binary numbers to the left increasestheir value, and shifting to the right decreases their value. The increase or decrease in value is based onpowers of 2.A shift of one place to the left increases the value by a power of 2, which in effect is multiplying thenumber by 2. To demonstrate this, let’s assume that the following block diagram is a 5-bit shift registercontaining the binary number 01100.01100Shifting the entire number one place to the left will put the register in the following condition:11000The binary number 01100 has a decimal equivalent of 12. If we convert 11000_{2} to decimal, we find ithas a value of 24_{10}. By shifting the number one place to the left, we have multiplied it by 2. A shift of twoplaces to the left would be the equivalent of multiplying the number by 2^{2}, or 4; three places by 2^{3}, or 8;and so forth.Shifting a binary number to the right decreases the value of the number by a power of 2 for eachplace. Let’s look at the same 5-bit register containing 01100_{2} and shift the number to the right.01100A shift of one place to the right will result in the register being in the following condition:00110By comparing decimal equivalents you can see that we have decreased the value from 12_{10} to 6_{10}.We have effectively divided the number by 2. A shift of two places to the right is the equivalent ofdividing the number by 2^{2}, or 4; three places by 2^{3}; or 8; and so forth.

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