Answer:
- 1010₂ = 10₁₀
- 1010₁₀ = 1111110010₂
Explanation:
You want to know the value of 1010 in binary.
Conversion to binary
We're not sure if you have the base ten number 1010 and you want its value in binary, or if the number 1010 is in binary, and you want its value in base ten.
Converting the base ten number to binary means looking at the remainders from division by 2, until the quotient is zero.
- 1010/2 = 505 r 0
- 505/2 = 252 r 1
- 252/2 = 126 r 0
- 126/2 = 63 r 0
- 63/2 = 31 r 1
- 31/2 = 15 r 1
- 15/2 = 7 r 1
- 7/2 = 3 r 1
- 3/2 = 1 r 1
- 1/2 = 0 r 1
The binary value is the list of these remainders from the bottom up:
1010₁₀ = 11 1111 0010₂
(It is often convenient for readability to group the digits by 3 or 4.)
Conversion from binary
The conversion from binary essentially uses the expanded form of the number. The arithmetic is done in the base you're converting to. Here, that's base ten.
1010₂ = 1×2³ +0×2² +1×2¹ +0×2⁰ = 8 +2 = 10
1010₂ = 10₁₀