2. Переведите числа в 10 СС: 1) 101001112 = ?10 2) 2648 = ?10 3) 1AC616 = ?10

Решение:

• 1) 10100111₂
  • $$10100111_2 = 1 imes 2^7 + 0 imes 2^6 + 1 imes 2^5 + 0 imes 2^4 + 0 imes 2^3 + 1 imes 2^2 + 1 imes 2^1 + 1 imes 2^0$$
  • $$= 128 + 0 + 32 + 0 + 0 + 4 + 2 + 1 = 167_{10}$$
• 2) 264₈
  • $$264_8 = 2 imes 8^2 + 6 imes 8^1 + 4 imes 8^0$$
  • $$= 2 imes 64 + 6 imes 8 + 4 imes 1 = 128 + 48 + 4 = 180_{10}$$
• 3) 1AC6₁₆
  • $$1AC6_{16} = 1 imes 16^3 + A imes 16^2 + C imes 16^1 + 6 imes 16^0$$
  • $$= 1 imes 4096 + 10 imes 256 + 12 imes 16 + 6 imes 1$$
  • $$= 4096 + 2560 + 192 + 6 = 6854_{10}$$

Ответ: 1) 167₁₀; 2) 180₁₀; 3) 6854₁₀