Convert binary numbers to numerical value? - Answers

Binary is simply the same number system we use, except it's base-2 instead of base-10. Therefore, the first position is worth 1, the second worth 2, the third worth 4, and so on. Each position doubles in value. If that position is filled with a 1, then that value is added to the overall value. If it's filled with a 0, than that value isn't added. This way, any number can be displayed. For example, take the number 1011. This might seem difficult, but it's really not. Start with the left place. It's worth 1, and filled with a 1, so we start with 1. The next place, worth 2, is also filled with a 1, so we add 2 to get 3. The next place, worth 4, is filled with 0, so we add nothing, and remain at 3. The next place, worth 8, is filled with a 1, so we add 8 to get 11. Therefore, 1011 in binary is 11 in normal numbers. Try the next one: 1100101001 This looks long and hard, but it's really not, when you take it apart. This number, when you work through it, boils down to 1 + 8 + 32 + 256 + 512. This equals 297 + 512, or 809. Therefore, 1100101001 in binary is 809 in regular numbers.