Question

Convert: a) 5810 to base 2 b) 101112 to base 10 Step by step would be awesome

Answer 1

I suppose you mean to convert 58₁₀ to base 2, and not 5810₁₀ to base 2.

Write 58 as the sum of the largest powers of 2 that you can:

58 = 32 + 26

58 = 32 + 16 + 10

58 = 32 + 16 + 8 + 2

58 = 2⁵ + 2⁴ + 2³ + 2¹

58 = 1×2⁵ + 1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰

⇒   58₁₀ = 111010₂

To convert from base 2 to base 10, write out and simplify the decimal expansion as in the last line of the previous example.

10111₂ = 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 1×2⁰

10111₂ = 16 + 0 + 4 + 2 + 1

⇒   10111₂ = 23₁₀

Answer 2

#a

$\\ \sf\Rrightarrow (58)_{10}$

$\\ \sf\Rrightarrow (2+8+16+32)_{10}$

$\\ \sf\Rrightarrow (2^1+2^3+2^4+2^5)_{10}$

$\\ \sf\Rrightarrow 0(2^0) 1(2^1)+0(2^2)+1(2^3)+1(2^4)+1(2^5)$

$\\ \sf\Rrightarrow (111010)_2$

#b

$\\ \sf\Rrightarrow (10111)_2$

$\\ \sf\Rrightarrow 1\times 2^0+1\times 2^1+1\times 2^2+0\times 2^3+1\times 2^4$

$\\ \sf\Rrightarrow 1+2+4+16$

$\\ \sf\Rrightarrow (23)_{10}$