State the denary representation of the binary number 10010111

Short answer: 151

Long answer: Students will be used to thinking in denary numbers so I would talk about what denary ( or base 10 ) actually means.

Basically each position is multiplied by 10 to the power of the position from right to left.

For example if we have the denary number 987

it is the same as saying 7 x 10^0 (for the first position), or seven lots of 1 plus 8 x 10^1, or eight lots of 10 plus 9 x 10^2, or nine lots of 100

which results in 987.

Binary works exactly the same except instead of 10^(the position) we have 2 to the power of the position.

So for our number 10010111 we can break it down into it's positions so from right to left we have

1x2^0, 1 (it is a general rule that anything to the power of 0 is 1) 1x2^1, 2 1x2^2, 4 0x2^3, 0 1x2^4, 16 0x2^5, 0 0x2^6, 0 1x2^7, 128

summing these: 1 + 2 +4 + 16 + 128 = 151 our answer

and so we can stop here.