4. Выполнить вычитание.

а) 1111110₂ - 1111011₂ = 11₂;

_1111110

1111011

11

Проверка:

1111110₂ = 1 × 2⁶ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × 2¹ = 64 + 32 + 16 + 8 + + 4 +2 = 126₁₀

1111011₂ = 1 × 2⁶ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2¹ + 1 × 2⁰ = 64 + 32 + 16 + 8 + + 2 + 1 = 123₁₀

11₂ = 1 × 2¹ + 1 × 2⁰ = 2 + 1 = 3₁₀

126₁₀ – 123₁₀ = 3₁₀

б) 1111100000₂ - 111110011₂ = 111101101₂;

_1111100000

111110011

111101101

Проверка:

1111100000₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ = 512 + 256 + 128 + 64 + + 32 = 992₁₀

111110011₂ = 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2¹ + 1 × 2⁰ = 256 + 128 + + 64 + 32 + 2 + 1 = 499₁₀

111101101₂ = 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁵ + 1 × 2³ + 1 × 2² + 1 × 2⁰ = 256 + 128 + 64 + 32 + 8 +4 + 1 = 493₁₀

992₁₀ - 499₁₀ = 493₁₀

в) 1111011111,1001₂ - 1010111100,01₂ = 100100011,0101₂;

_1111011111,1001

1010111100,0100

100100011,0101

Проверка:

1111011111,1001₂ = 1 × 2⁹ + 1 × 2⁸ + 1 × 2⁷ + 1 × 2⁶ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × × 2¹ + 1 × 2⁰ + 1 × 2^-1 + + 1 × 2^-4 = 512 + 256 + 128 + 64 + 16 + 8 + 4 + 2 + 1 + 0,5 + 0,0625 = 991,5625₁₀

1010111100,0100₂ = 1 × 2⁹ + 1 × 2⁷ + 1 × 2⁵ + 1 × 2⁴ + 1 × 2³ + 1 × 2² + 1 × 2^-2 = = 512 + 128 + 32 + 16 + + 8 + 4 + 0,25= 700,25₁₀

100100011,0101₂ = 1 × 2⁸ + 1 × 2⁵ + 1 × 2¹ + 1 × 2⁰ + 1 × 2^-2 + 1 × 2^-4 = 256 + 32 + + 2 + 1 + 0,25 + 0,0625= 291,3125₁₀

991,5625₁₀ - 700,25₁₀ = 291,3125₁₀

г) 1241,34₈ - 1124,3₈ = 115,04₈;

_1241,34

1124,30

115,04

Проверка:

1241,34₈ = 1 × 8³ + 2 × 8² + 4 × 8¹ + 1 × 8⁰ + 3 × 8^-1 + 4 × 8^-2 = 512 + 128 + 32 + 1 + + 0,375 + 0,0625 = 673,4375₁₀

1124,30₈ = 1 × 8³ + 1 × 8² + 2 × 8¹ + 4 × 8⁰ + 3 × 8^-1 = 512 + 64 + 16 + 4 + 0,375 = = 596,375₁₀

115,04₈= 1 × 8² + 1 × 8¹ + 5 × 8⁰ + 4 × 8^-2 = 64 + 8 + 5 + 0,0625 = 77,0625₁₀

673,4375₁₀ - 596,375₁₀ = 77,0625₁₀

д) 15F,A₁₆ - 159,4₁₆ = 6,6₁₆.

_15F,A

159,4

6,6

Проверка:

15F,A ₁₆ = 1 × 16² + 5 × 16¹ + 15 × 16⁰ + 10 × 16^-1 = 256 + 80 + 15 + 0,625 = = 351,625₁₀

159,4₁₆ = 1 × 16² +5 × 16¹ +9 × 16⁰ + 4 × 16^-1 = 256 + 80 + 9 + 0,25 = 345,25₁₀

6,6₁₆ = 6 × 16⁰ + 6 × 16^-1 = 6,375₁₀

351,625₁₀ - 345,25₁₀ = 6,375₁₀

5. Выполнить умножение.

а) 1001010₂ 1101111₂ = 10000000010110₂;

_×1001010

1101111

1101111

+ 1101111

1101111

10000000010110

Проверка:

1101111₂ = 1 × 2⁶ + 1 × 2⁵ + 1 × 2³ + 1 × 2² + 1 × 2¹ + 1 × 2⁰ = 64 + 32 + 8 + 4 + 2 + + 1 = 111₁₀

1001010₂ = 1 × 2⁶ + 1 × 2³ + 1 × 2¹ = 64 + 8 + 2 = 74₁₀

10000000010110₂ = 1 × 2¹³ + 1 × 2⁴ + 1 × 2² + 1 × 2¹ = 8192 + 16 + 4 + 2 = 8214₁₀

111₁₀ × 74₁₀ = 8214₁₀

б) 1616,3₈ 61,3₈ = 127625,61₈;

1616,3

61,3

52531

+ 16163

125262 1

127625,61

Проверка:

1616,3₈ = 1 × 8³ + 6 × 8² + 1 × 8¹ + 6 × 8⁰ + 3 × 8^-1 = 512 + 384 + 8 + 6 + 0,375 = = 910,375₁₀

61,3₈ = 6 × 8¹ + 1 × 8⁰ + 3 × 8^-1 = 48 + 1 + 0,375 = 49,375₁₀

127625,61₈= 1 × 8⁵ + 2 × 8⁴ + 7 × 8³ + 6 × 8² + 2 × 8¹ + 5 × 8⁰ + 6 × 8^-1 + 1 × 8^-2 = = 32768 + 8192 + 3584 + + 384 + 16 + 5 + 0,75 + 0,015625= 44949,765625₁₀

910,375₁₀ × 49,375₁₀ = 44949,765625₁₀

в) 3A,38₁₆ 64,4₁₆ = 16CC,6E₁₆.

_×3A,38

64,40

E8E0

+ E8E0

15D50 1

16CC,6E0

Проверка:

3A,38₁₆ = 3 × 16² + 10 × 16¹ + 3 × 16⁰ + 8 × 16^-1 = 48 + 10 + 0,1875 + 0,03125 = = 58,21875₁₀

64,4₁₆ = 6 × 16¹ +4 × 16⁰ +4 × 16^-1 = 96 + 4 + 0,25 = 100,25₁₀

16CC,6E₁₆= 1 × 16³ + 6 × 16² + 12 × 16¹ + 12 × 16⁰ + 1 × 16^-1 + 6 × 16^-2 = 4096 + + 1536 + 192 + 12 + 0,375 + 0,046875 =5836,4296875₁₀

58,21875₁₀ × 100,25₁₀ = 5836,4296875₁₀