Division by 7 without using the divide operator

[Justin.Velazquez]

Hello everyone,

I'm not really new to programming but my bitwise skills definately need
work.
I came across a problem I've been trying to figure out for fun. I'm
trying to write
a routine that will divide a number by 7 without using the divide
operator. I
figured how to multiply by 7 using bitwise operators ( (x << 3) - x )
but I having
a hard time trying to figure a bitwise approach to do the divide. The
closed I've
been able to come is:

((x>> 3) + x) >> 3

This works for most cases but not all. Am I approaching this problem
wrong?
is it possible to divide by 7 using bitwise operators? Any advice or
help would be
greatly appreciated.

Thanks
justin

 

[Alf P. Steinbach]

* (e-mail address removed):

Hello everyone,

I'm not really new to programming but my bitwise skills definately need
work.
I came across a problem I've been trying to figure out for fun. I'm
trying to write
a routine that will divide a number by 7 without using the divide
operator. I
figured how to multiply by 7 using bitwise operators ( (x << 3) - x )
but I having
a hard time trying to figure a bitwise approach to do the divide. The
closed I've
been able to come is:

((x>> 3) + x) >> 3

This works for most cases but not all. Am I approaching this problem
wrong?
is it possible to divide by 7 using bitwise operators? Any advice or
help would be
greatly appreciated.

Your draft solution can be approximated as (x/8+x)/8 = (9x/8)/8=(9/64)x.
Since 9 decimal = 1001 binary, and since 1/64 = 0.000001 binary, that
is essentially the same as multiplying x by 1001*0.000001 = 0.001001
binary, wheras 1/7 = 0.0010010010010010... binary. Perhaps you can see
a pattern both in that expansion and in your first draft solution?