Binary shift

• There are two types of binary shifts, logical and arithmetic
  • A logical shift is used for multiplying or dividing a binary number
    • Digits are shifted to the left to multiply, and to the right to divide
      • The shifts multiply or divide by two, depending on the direction

        • For example, to multiple 12 by two:

          32	16	8	4	2	1
          0	0	1	1	0	0	= 12

          Shift to the left

          32	16	8	4	2	1
          0	1	1	0	0	0	= 24

        • For example, to divide 12 by two:

          32	16	8	4	2	1
          0	0	1	1	0	0	= 12

          Shift to the right

          32	16	8	4	2	1
          0	0	0	1	1	0	= 6

  • An arithmetic shift is used for multiplying or dividing a signed binary number
    • Apart from being used for signed numbers, they are identical to logical shifts

      • For example, to multiple -12 by two:

        MSB	32	16	8	4	2	1
        0	0	0	1	1	0	0	= 12

        Convert 12 to negative

        MSB	32	16	8	4	2	1
        1	1	1	0	0	1	1	= -13

        Add 1

        MSB	32	16	8	4	2	1
        1	1	1	0	1	0	0	= -12

        Shift to the left

        MSB	32	16	8	4	2	1
        1	1	0	1	0	0	0	= -24