Question

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Numbering Systems Assignment

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Binary/decimal conversion:

101110101 in binary = ______________ in decimal

272 in decimal = _____________________________ in binary

101100110011 in binary = _____________ in decimal

361 in decimal = _____________________ in binary

Hexadecimal/decimal conversion:

E8 in hexadecimal = __________________ in decimal

516 in decimal = _______________________ in hexadecimal

ACF in hexadecimal = _______________________ in decimal

7815 in decimal = _______________ in hexadecimal

Binary/hexadecimal conversion:

1101001111001111101 in binary = _____________ in hex

F9D in hex = ___________________ in binary

1001100010101110110110101111 in binary = _______________ in hex

E45C in hex = _______________________in binary

Answer 1

Binary/decimal conversion:

101110101 in binary = ______________ in decimal

= 1*2⁸ + 1*2⁶ + 1*2⁵ + 1*2⁴ + 1*2² + 1*2⁰ = 256 + 64+ 32 + 16+ 4+ 1= 373 in decimal

272 in decimal = _____________________________ in binary

   remainder

2| 272

2| 136 0

2| 68 0

2|34    0

2|17    0

2|8 1

2|4 0

2|2 0

2|1    0

2|0    1

in reverse direction take remainders = 100010000

101100110011 in binary = _____________ in decimal

1*2¹¹ + 1*2⁹ + 1*2⁸ + 1*2⁵ + 1*2⁴ + 1*2¹ + 1*2⁰ = 2048 + 512 + 256 + 32 + 16 + 2+ 1 = 2867 in decimal

361 in decimal = _____________________ in binary

remainder

2|361

2|180    1

2|90    0

2|45    0

2|22 1

2|11 0

2|5 1

2| 2 1

2|1 0

2|0 1

= 101101001 in binary

Hexadecimal/decimal conversion:

E8 in hexadecimal = __________________ in decimal

E8 = 1110 1000 in binary

= 1*2⁷ + 1*2⁶ + 1*2⁵ + 1*2^{3 =} 128 + 64+ 32 + 8 = 232 in decimal

516 in decimal = _______________________ in hexadecimal

16|516

16|32    4

16|2 0

16|0    2

= 204 in hexadecimal

ACF in hexadecimal = _______________________ in decimal

= A * 16² + C * 16¹ + F * 16⁰ = 10 * 256 + 12 * 16 + 15 = 2767 in decimal

7815 in decimal = _______________ in hexadecimal

16| 7815

16|488 7

16|30 8

16|1    E

16| 0 1

= 1E87 in hexadecimal

Binary/hexadecimal conversion:

1101001111001111101 in binary = _____________ in hex

110 1001 1110 0111 1101 = 69E7D

F9D in hex = ___________________ in binary

F = 1111

9 = 1001

D = 1101

= 111110011101 in binary

1001100010101110110110101111 in binary = _______________ in hex

1001 1000 1010 1110 1101 1010 1111 = 98AEDAF

E45C in hex = _______________________in binary

E = 1110

4 = 0100

5 = 0101

C = 1100

= 1110010001011100 in binary

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