2. Перевести данное число в десятичную систему счисления.

а) 1000110110₂ = 566₁₀;

1000110110₂ = 1 × 2⁹ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2² + 1 × 2¹ = 512 + 32 + 16 + 4 + 2 = 566₁₀

б) 111100001₂ = 481₁₀;

111100001₂ = 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2⁰ = 256 + 128 + 64 + 32 + 1 = 481₁₀

в) 1110010100,1011001₂ = 916,69531₁₀;

1110010100,1011001₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁴ + 1 × 2² + 1 × 2^-1 + 1 × 2^-3 + + 1 × 2^-4 + 1 × 2^-7 = 512 + 256 + 128 + 4 + 0,5 + 0,125 + 0,0625 + 0,0078125 =916,69531₁₀

г) 1000000110,00101₂ = 518,15625₁₀;

1000000110,00101₂ = 1 × 2⁹ + 1 × 2² + 1 × 2¹ + 1 × 2^-3 + 1 × 2^-5 = 512 + 4 + 2 + 0,125 + + 0,03125 = 518,15625₁₀

д) 666,16₈ = 438,21875₁₀;

666,16₈ = 6 × 8² + 6 × 8¹ + 6 × 8⁰ +1 × 8^-1 + 6 × 8^-2 =384 + 48 + 6 + 0,125 + 0,09375 = = 438,21875₁₀

е) 1C7,68₁₆ = 455,40625₁₀.

1C7,68₁₆ = 1 × 16² + 12 × 16¹ + 7 × 16⁰ + 6 × 16^-1 + 8 × 16^-2 = 256 + 192 + 7 + 0,375 + + 0,03125 = 455,40625₁₀

3. Сложить числа.

а) 1101010000₂ + 1011101001₂ = 11000111001₂;

₊1101010000

1011101001

11000111001

Проверка:

1101010000₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁶ + 1 × 2⁴ = 512 + 256 + 64 + 16 = 848₁₀

1011101001₂ = 1 × 2⁹ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2³ + 1 × 2⁰ = 512 + 128 + 64 + + 32 + 8 + 1 = 745₁₀

11000111001₂ = 1 × 2¹⁰ + 1 × 2⁹ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2⁰ = 1024 + 512 + 32 + + 16 + 8 + 1 = 1593₁₀

848₁₀ + 745₁₀ = 1593₁₀

б) 100000101₂+1100001010₂ = 10000001111₂;

₊100000101

1100001010

10000001111

Проверка:

100000101₂ = 1 × 2⁸ + 1 × 2² + 1 × 2⁰ = 256 + 4 + 1 = 261₁₀

1100001010₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2³ + 1 × 2¹ = 512 + 256 + 8 + 2 = 778₁₀

10000001111₂ = 1 × 2¹⁰ + 1 × 2³ + 1 × 2² + 1 × 2¹ + 1 × 2⁰ = 1024 + 8 + 4 + 2 + 1 = 1039₁₀

261₁₀ + 778₁₀ = 1039₁₀

в) 1100100001,01001₂ + 1110111111,011₂ = 11011100000,10101₂;

₊ 1100100001,01001

1110111111,01100

11011100000,10101

Проверка:

1100100001,01001₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁵ + 1 × 2⁰ + 1 × 2^-2 + 1 × 2^-5 = 512 + + 256 + 32 + 1 + 0,25 + 0,03125 = 801,28125₁₀

1110111111,01100₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × × 2¹ + 1× 2⁰ + 1 × 2^-2 +1 × 2^-3 = 512 + 256 + 128 +32 + 16 + 8 + 4 +2 +1 + 0,251 + + 0,125 = 959,375₁₀

11011100000,10101₂ = 1 × 2¹⁰ + 1 × 2⁹ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2^-1 + 1 × 2^-3 + 1 × × 2^-5 = 1024 + 512 + 128 + 64 + 32 + 0,5 + 0,125 + 0,03125 = 1760,65625₁₀

801,28125₁₀ + 959,375₁₀ = 1760,65625₁₀

г) 242,2₈ + 1153,5₈ = 1415,7₈;

₊1153,5

242,2

1415,7

Проверка:

1153,5₈ = 1 × 8³ + 1 × 8² + 5 × 8¹ + 3 × 8⁰ + 5 × 8^-1 = 512 + 64 + 40 + 3 + 0,625 = 619,625₁₀

242,2₈ = 2 × 8² + 4 × 8¹ + 2 × 8⁰ + 2 × 8^-1 = 128 + 32 + 2 + 0,25 = 162,25₁₀

1415,7₈= 1 × 8³ + 4 × 8² + 1 × 8¹ + 5 × 8⁰ + 7 × 8^-1 = 512 + 256 + 8 + 5 + 0,875 = 781,875₁₀

619,625₁₀ + 162,25₁₀ = 781,875₁₀

д) 84,8₁₆ + 27E,8₁₆ = 303₁₆.

₊27E,8

84,8

303,0

Проверка:

84,8₁₆ = 8 × 16¹ + 8 × 16⁰ + 8 × 16^-1 = 128 + 4 + 0,5 = 132, 5₁₀

27E,8₁₆ = 2 × 16² +7 × 16¹ +14 × 16⁰ + 8 × 16^-1 = 512 + 112 + 14 + 0,5 = 638, 5₁₀

303₁₆ = 3 × 16² + 3 × 16⁰ = 768 + 3 = 771₁₀

132, 5₁₀ + 638, 5₁₀ = 771₁₀