How can you product binary numbers?

Answer 1

Each place value column in a binary number can have only one of two values: 0 or 1; thus the counting numbers in binary are:

1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, ...

To product (or multiply) binary numbers, use long multiplication like normal, but when adding the columns together remember how binary counting goes (above) which means you may carry more than 1, in which case carry to more than one column, eg if the sum is 101 put a 1 under the column, carry 10 to the previous 2 columns (ie 0 to the next left column and 1 to the column to the left of that one).

example 1111 × 101 = 1001011 (in decimal 15 × 5 = 75)

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If you meant to produce binary numbers, that is convert decimal to binary, then the general algorithm to convert between bases works:

1. divide the number by the new base to get a whole number quotient and a remainder
2. note the remainder
3. replace the number by the quotient
4. if the number is not zero repeat from step 1
5. write the remainders in reverse order to get the original number in the new base.

For binary, the new base is 2.

Example 75 in binary:

75 ÷ 2 = 37 r 1

37 ÷ 2 = 18 r 1

18 ÷ 2 = 9 r 0

9 ÷ 2 = 4 r 1

4 ÷ 2 = 2 r 0

2 ÷ 2 = 1 r 0

1 ÷ 2 = 0 r 1

→ 75 in binary is 1001011

To convert from binary to decimal remember that each place value column of a binary number has twice the value of the column to its right; add the value of each column by its binary digit (bit).

eg 1001011 = (1 × 64) + (0 × 32) + (0 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 64 + 8 + 2 + 1 = 75

It may be easier to start from the right hand end of the number and work left as then you start with the place column value of 1 and multiply it by 2 each time:

eg 1001011 = (1 × 1) + (1 × 2) + (0 × 4) + (1 × 8) + (0 × 16) +( 0 × 32) + (1 × 64) = 1 + 2 + 8 + 64 = 75