Question

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Answer 1

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Number System

1. $\sf (1234)10$

➝ $\sf 1 \times 10^3 + 2 \times 10^2 + 3 × 10^1 + 4 \times 10^{\circ}$

➝ $\sf 1000 + 200 + 30 + 4$

➝ $\sf 1207$

━━━━━━━━━━━━━━━━

2. $\sf (1010)2$

➝ $\sf 1 \times 10^3 + 0 \times 10^2+ 1 \times 10^1+ 0 \times 10^{\circ}$

➝ $\sf 1000+0+10+0$

➝ $\sf 1010$

━━━━━━━━━━━━━━━━

3. $\sf (357)8$

➝ $\sf 3 \times 8^{2} + 5\times 8^1+7\times 8^{\circ}$

➝ $\sf 3\times 64 + 40 + 7$

➝ $\sf 192+40+7$

➝ $\sf 239$

━━━━━━━━━━━━━━━━

4. $\sf (560)8$

➝ $\sf 5\times8^2+ 6\times8^1+ 0\times 8^{\circ}$

➝ $\sf 5\times 64+6\times 8+0$

➝ $\sf 320 + 48$

➝ $\sf 368$

━━━━━━━━━━━━━━━━

5. $\sf (50)16$

➝ $\sf 5\times 16^1+0\times 16^{\circ}$

➝ $\sf 80 + 0$

➝ $\sf 80$

━━━━━━━━━━━━━━━━

Number System Conversion

1. Decimal to Binary $\sf (78) = ()2$

➳ $\sf (78) = (x)2$

➳ $\sf x.2^1+x.2^{\circ} =78$

➳ $\sf 2x + x = 78$

➳ $\sf 3x = 78$

➳ $\sf x = \dfrac{78}{3}$

➳ $\sf x= 29$

━━━━━━━━━━━━━━━━

2. Decimal to Octal $\sf (45)= ()8$

➳ $\sf (45) = (x)8$

➳ $\sf x.8^1+x.8^{\circ} =45$

➳ $\sf 8x + x = 45$

➳ $\sf 9x = 45$

➳ $\sf x = \dfrac{45}{9}$

➳ $\sf x= 5$

━━━━━━━━━━━━━━━━

3. Decimal to Hexadecimal $\sf (55) = ()16$

➳ $\sf (55) = (x)16$

➳ $\sf x.16^1+x.16^{\circ} =55$

➳ $\sf 16x + x = 55$

➳ $\sf 17x = 55$

➳ $\sf x = \dfrac{55}{17}$

➳ $\sf x= 3.25 \approx 4$

➳ $\sf x = 4$

━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

NumberSystem:−

1. (1234)10

= 1 × 10³ + 2× 10² + 3 × 10¹ + 4 × 10°

= 1000 + 200 + 30 + 4

= 1207

2.(1010)2

= 1 × 10³ + 0 × 10² + 1 × 10¹ + 0 × 10°

= 1000+0+10+0

=1010

3.(357)8

= 3×8² + 5×8¹ + 7×8°

= 3×64 + 40 + 7

=192+40+7

=239

4.(560)8

= 5×8² + 6×8¹ + 0×8°

= 5×64+6×8+0

= 320 + 48

= 368

5.(50)16

= 5×16¹ + 0×16°

= 80 + 0

= 80

\mathtt{\large{\underline {\red{Number\:System\:Conversion:-}}}}

NumberSystemConversion:−

1.)Decimal to Binary (78) = ()2

➡ (78) = (x)2

➡ x.2¹+x.2° =78

➡ 2x + x = 78

➡ 3x = 78

➡ x = 78/3

➡ x= 29

2. Decimal to Octal (45)= ()8

➡ (45) = (x)8

➡ x.8¹+x.8° =45

➡ 8x + x = 45

➡9x = 45

➡ x = 45/9

➡ x= 5

3. Decimal to Hexadecimal (55) = ()16

➡ (55) = (x)16

➡ x.16¹+x.16° =55

➡ 16x + x = 55

➡ 17x = 55

➡ x = 55/17

➡ x= 3.25 ≈ 4

➡ x = 4

hope it helps you.......❤️❤️