Binary numbers are multiplied and divided through a process called shifting.

Multiplication

To multiply a number, a binary shift moves all the digits in the binary number along to the left and fills the gaps after the shift with 0:

• to multiply by two, all digits shift one place to the left
• to multiply by four, all digits shift two places to the left
• to multiply by eight, all digits shift three places to the left
• and so on

Example - 1100 (denary 12) × 2

Result: shifting one place to the left gives 11000 (24 denary)

Example - 10110 (denary 22) × 4

Result: shifting two places to the left gives 1011000 (denary 88)

Division

To divide a number, a binary shift moves all the digits in the binary number along to the right:

• to divide by two, all digits shift one place to the right
• to divide by four, all digits shift two places to the right
• to divide by eight, all digits shift three places to the right
• and so on

Example - 100100 (denary 36) ÷ 2

Result: shifting one place to the right gives 10010 (denary 18)

Example - 1111 (denary 15) ÷ 2

Result: shifting two places to the right gives 111 (denary 7).

Note - 15 ÷ 2 = 7.5. However, in this form of binary, there are no decimals, and so the decimal is discarded.

Example - 110110 (denary 54) ÷ 4

Result: shifting two places to the right gives 1101 (denary 13)