The nearest thing on a camera to the magnification of a pair of binoculars is the viewfinder magnification. This tells you how large things appear when looking through the viewfinder, compared to the naked eye. Note that it tells you nothing about what is captured in the image.
On a 350D, for example, the viewfinder magnification is 0.8x with a 50mm lens. So, for 1x magnification you need a 62.5mm lens, and pro-rata thereafter. To get the same degree of magnification (through the viewfinder) as a pair of 8x binoculars you would need a 500mm lens.
Also note that the sensor size doesn't come into this - a 20D (1.6 format sensor, same as 350D) has a viewfinder magnification of 0.9x at 50mm and a 5D (full frame sensor) has 0.71x at 50mm.
Of course, most people don't worry much about viewfinder magnification on a digital camera as it doesn't tell you what the picture will contain. The apparent size of objects in the photo will obviously depend on how large you print/view the photo and from what distance you look at it. That cannot be related to the binocular magnification unless you specify a viewing size/distance.
The concept of the 'normal' lens (50mm on full frame, 31mm on a 1.6 factor sensor) says that you will get '1x magnification' (i.e. objects will appear same size as with the naked eye) with something like a 10x8 print at arms length. If those print viewing conditions are what you are interested in, then you can regard the 'normal' lens as giving 1x magnification for the print. Of course, in this case, things will look a lot smaller than 1x when you look through the camera viewfinder.