# Binary shifts

If a binary number is shifted to the left this is equivalent to multiplying the number by 2 for each shift to the left.

For example: if we shift

Two places to the left we get the binary number:

Notice how we moved the digits to the left and filled the gaps in the 8-bit binary number with zeros as we shifted left.

The original binary number has a value of 15 (i.e. 1+2+4+8 = 15); the number after shifting two places to the left has the value 60 (i.e. 32+16+8+4 = 60). It is multiplied by 4, or 22.

Shifting binary numbers to the right has the opposite effect i.e each shift to the right has the effect of dividing by 2.

### Multiplication and Division by powers of 2

This gives an easy way to multiply and divide binary numbers by the powers of two.

• Shifting right one place the number divides by 2
• Shifting left multiplies the number by 2

This is the equivalent of shifting a decimal number right or left - for example shifting 44000 right 1 place = 4400 (it divides the number by 10). Shifting left multiplies the number by 10.