Convert the following number systems from base 10 to base 2: 1) 19 101 247 99

Mathematics
Convert the following number systems from base 10 to base 2: 1) 19 101 247 99

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Answer

1001101102100110110_2

Step 1: Convert 31010310_{10} to base 2.
Repeatedly divide the number by 2 and record the remainders (read remainders from last to first).

310÷2=155 remainder 0,155÷2=77 remainder 1,77÷2=38 remainder 1,38÷2=19 remainder 0,19÷2=9 remainder 1,9÷2=4 remainder 1,4÷2=2 remainder 0,2÷2=1 remainder 0,1÷2=0 remainder 1.\begin{align*} 310 &\div 2 = 155 \ remainder\ 0, \\ 155 &\div 2 = 77 \ remainder\ 1, \\ 77 &\div 2 = 38 \ remainder\ 1, \\ 38 &\div 2 = 19 \ remainder\ 0, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 1001101102100110110_2.
310_{10 = 100110110_2
100110110_2

Step 2: Convert 31010310_{10} to base 8.

310÷8=38 remainder 6,38÷8=4 remainder 6,4÷8=0 remainder 4.\begin{align*} 310 &\div 8 = 38 \ remainder\ 6, \\ 38 &\div 8 = 4 \ remainder\ 6, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}

Remainders from bottom to top: 4668466_8.
310_{10 = 466_8
466_8

Step 3: Convert 31010310_{10} to base 16.

310÷16=19 remainder 6,19÷16=1 remainder 3,1÷16=0 remainder 1.\begin{align*} 310 &\div 16 = 19 \ remainder\ 6, \\ 19 &\div 16 = 1 \ remainder\ 3, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 13616136_{16}.
310_{10 = 136_{16}
136_{16}

Step 4: Convert 2510102510_{10} to base 2.

2510÷2=1255 remainder 0,1255÷2=627 remainder 1,627÷2=313 remainder 1,313÷2=156 remainder 1,156÷2=78 remainder 0,78÷2=39 remainder 0,39÷2=19 remainder 1,19÷2=9 remainder 1,9÷2=4 remainder 1,4÷2=2 remainder 0,2÷2=1 remainder 0,1÷2=0 remainder 1.\begin{align*} 2510 &\div 2 = 1255 \ remainder\ 0, \\ 1255 &\div 2 = 627 \ remainder\ 1, \\ 627 &\div 2 = 313 \ remainder\ 1, \\ 313 &\div 2 = 156 \ remainder\ 1, \\ 156 &\div 2 = 78 \ remainder\ 0, \\ 78 &\div 2 = 39 \ remainder\ 0, \\ 39 &\div 2 = 19 \ remainder\ 1, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 1001110011102100111001110_2.
2510_{10 = 100111001110_2
100111001110_2

Step 5: Convert 2510102510_{10} to base 8.

2510÷8=313 remainder 6,313÷8=39 remainder 1,39÷8=4 remainder 7,4÷8=0 remainder 4.\begin{align*} 2510 &\div 8 = 313 \ remainder\ 6, \\ 313 &\div 8 = 39 \ remainder\ 1, \\ 39 &\div 8 = 4 \ remainder\ 7, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}

Remainders from bottom to top: 471684716_8.
2510_{10 = 4716_8
4716_8

Step 6: Convert 2510102510_{10} to base 16.

2510÷16=156 remainder 14 (E),156÷16=9 remainder 12 (C),9÷16=0 remainder 9.\begin{align*} 2510 &\div 16 = 156 \ remainder\ 14 \ (E), \\ 156 &\div 16 = 9 \ remainder\ 12 \ (C), \\ 9 &\div 16 = 0 \ remainder\ 9. \end{align*}

Remainders from bottom to top: 9CE169CE_{16}.
2510_{10 = 9CE_{16}
9CE_{16}

Step 7: Convert 28210282_{10} to base 2.

282÷2=141 remainder 0,141÷2=70 remainder 1,70÷2=35 remainder 0,35÷2=17 remainder 1,17÷2=8 remainder 1,8÷2=4 remainder 0,4÷2=2 remainder 0,2÷2=1 remainder 0,1÷2=0 remainder 1.\begin{align*} 282 &\div 2 = 141 \ remainder\ 0, \\ 141 &\div 2 = 70 \ remainder\ 1, \\ 70 &\div 2 = 35 \ remainder\ 0, \\ 35 &\div 2 = 17 \ remainder\ 1, \\ 17 &\div 2 = 8 \ remainder\ 1, \\ 8 &\div 2 = 4 \ remainder\ 0, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 1000110102100011010_2.
282_{10 = 100011010_2
100011010_2

Step 8: Convert 28210282_{10} to base 8.

282÷8=35 remainder 2,35÷8=4 remainder 3,4÷8=0 remainder 4.\begin{align*} 282 &\div 8 = 35 \ remainder\ 2, \\ 35 &\div 8 = 4 \ remainder\ 3, \\ 4 &\div 8 = 0 \ remainder\ 4. \end{align*}

Remainders from bottom to top: 4328432_8.
282_{10 = 432_8
432_8

Step 9: Convert 28210282_{10} to base 16.

282÷16=17 remainder 10 (A),17÷16=1 remainder 1,1÷16=0 remainder 1.\begin{align*} 282 &\div 16 = 17 \ remainder\ 10 \ (A), \\ 17 &\div 16 = 1 \ remainder\ 1, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 11A1611A_{16}.
282_{10 = 11A_{16}
11A_{16}

Step 10: Convert 4990104990_{10} to base 2.

4990÷2=2495 remainder 0,2495÷2=1247 remainder 1,1247÷2=623 remainder 1,623÷2=311 remainder 1,311÷2=155 remainder 1,155÷2=77 remainder 1,77÷2=38 remainder 1,38÷2=19 remainder 0,19÷2=9 remainder 1,9÷2=4 remainder 1,4÷2=2 remainder 0,2÷2=1 remainder 0,1÷2=0 remainder 1.\begin{align*} 4990 &\div 2 = 2495 \ remainder\ 0, \\ 2495 &\div 2 = 1247 \ remainder\ 1, \\ 1247 &\div 2 = 623 \ remainder\ 1, \\ 623 &\div 2 = 311 \ remainder\ 1, \\ 311 &\div 2 = 155 \ remainder\ 1, \\ 155 &\div 2 = 77 \ remainder\ 1, \\ 77 &\div 2 = 38 \ remainder\ 1, \\ 38 &\div 2 = 19 \ remainder\ 0, \\ 19 &\div 2 = 9 \ remainder\ 1, \\ 9 &\div 2 = 4 \ remainder\ 1, \\ 4 &\div 2 = 2 \ remainder\ 0, \\ 2 &\div 2 = 1 \ remainder\ 0, \\ 1 &\div 2 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 100110111111021001101111110_2.
4990_{10 = 1001101111110_2
1001101111110_2

Step 11: Convert 4990104990_{10} to base 8.

4990÷8=623 remainder 6,623÷8=77 remainder 7,77÷8=9 remainder 5,9÷8=1 remainder 1,1÷8=0 remainder 1.\begin{align*} 4990 &\div 8 = 623 \ remainder\ 6, \\ 623 &\div 8 = 77 \ remainder\ 7, \\ 77 &\div 8 = 9 \ remainder\ 5, \\ 9 &\div 8 = 1 \ remainder\ 1, \\ 1 &\div 8 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 11576811576_8.
4990_{10 = 11576_8
11576_8

Step 12: Convert 4990104990_{10} to base 16.

4990÷16=311 remainder 14 (E),311÷16=19 remainder 7,19÷16=1 remainder 3,1÷16=0 remainder 1.\begin{align*} 4990 &\div 16 = 311 \ remainder\ 14 \ (E), \\ 311 &\div 16 = 19 \ remainder\ 7, \\ 19 &\div 16 = 1 \ remainder\ 3, \\ 1 &\div 16 = 0 \ remainder\ 1. \end{align*}

Remainders from bottom to top: 137E16137E_{16}.
4990_{10 = 137E_{16}
137E_{16}

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Quick Answer

Convert 310_10 to base 2. Repeatedly divide the number by 2 and record the remainders (read remainders from last to first).

Convert the following number systems from base 10 to base 2: 1) 19 101 247 99
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Step 1: Convert 310_10 to base 2. Repeatedly divide the number by 2 and record the remainders (read remainders from last to first). 310 &÷ 2 = 155 \ remainder\ 0, \\ 155 &÷ 2 = 77 \ remainder\ 1, \\ 77 &÷ 2 = 38 \ remainder\ 1, \\ 38 &÷ 2 = 19 \ remainder\ 0, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100110110_2. 310_10 = 100110110_2 100110110_2 Step 2: Convert 310_10 to base 8. 310 &÷ 8 = 38 \ remainder\ 6, \\ 38 &÷ 8 = 4 \ remainder\ 6, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 466_8. 310_10 = 466_8 466_8 Step 3: Convert 310_10 to base 16. 310 &÷ 16 = 19 \ remainder\ 6, \\ 19 &÷ 16 = 1 \ remainder\ 3, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 136_16. 310_10 = 136_16 136_16 Step 4: Convert 2510_10 to base 2. 2510 &÷ 2 = 1255 \ remainder\ 0, \\ 1255 &÷ 2 = 627 \ remainder\ 1, \\ 627 &÷ 2 = 313 \ remainder\ 1, \\ 313 &÷ 2 = 156 \ remainder\ 1, \\ 156 &÷ 2 = 78 \ remainder\ 0, \\ 78 &÷ 2 = 39 \ remainder\ 0, \\ 39 &÷ 2 = 19 \ remainder\ 1, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100111001110_2. 2510_10 = 100111001110_2 100111001110_2 Step 5: Convert 2510_10 to base 8. 2510 &÷ 8 = 313 \ remainder\ 6, \\ 313 &÷ 8 = 39 \ remainder\ 1, \\ 39 &÷ 8 = 4 \ remainder\ 7, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 4716_8. 2510_10 = 4716_8 4716_8 Step 6: Convert 2510_10 to base 16. 2510 &÷ 16 = 156 \ remainder\ 14 \ (E), \\ 156 &÷ 16 = 9 \ remainder\ 12 \ (C), \\ 9 &÷ 16 = 0 \ remainder\ 9. Remainders from bottom to top: 9CE_16. 2510_10 = 9CE_16 9CE_16 Step 7: Convert 282_10 to base 2. 282 &÷ 2 = 141 \ remainder\ 0, \\ 141 &÷ 2 = 70 \ remainder\ 1, \\ 70 &÷ 2 = 35 \ remainder\ 0, \\ 35 &÷ 2 = 17 \ remainder\ 1, \\ 17 &÷ 2 = 8 \ remainder\ 1, \\ 8 &÷ 2 = 4 \ remainder\ 0, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100011010_2. 282_10 = 100011010_2 100011010_2 Step 8: Convert 282_10 to base 8. 282 &÷ 8 = 35 \ remainder\ 2, \\ 35 &÷ 8 = 4 \ remainder\ 3, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 432_8. 282_10 = 432_8 432_8 Step 9: Convert 282_10 to base 16. 282 &÷ 16 = 17 \ remainder\ 10 \ (A), \\ 17 &÷ 16 = 1 \ remainder\ 1, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 11A_16. 282_10 = 11A_16 11A_16 Step 10: Convert 4990_10 to base 2. 4990 &÷ 2 = 2495 \ remainder\ 0, \\ 2495 &÷ 2 = 1247 \ remainder\ 1, \\ 1247 &÷ 2 = 623 \ remainder\ 1, \\ 623 &÷ 2 = 311 \ remainder\ 1, \\ 311 &÷ 2 = 155 \ remainder\ 1, \\ 155 &÷ 2 = 77 \ remainder\ 1, \\ 77 &÷ 2 = 38 \ remainder\ 1, \\ 38 &÷ 2 = 19 \ remainder\ 0, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 1001101111110_2. 4990_10 = 1001101111110_2 1001101111110_2 Step 11: Convert 4990_10 to base 8. 4990 &÷ 8 = 623 \ remainder\ 6, \\ 623 &÷ 8 = 77 \ remainder\ 7, \\ 77 &÷ 8 = 9 \ remainder\ 5, \\ 9 &÷ 8 = 1 \ remainder\ 1, \\ 1 &÷ 8 = 0 \ remainder\ 1. Remainders from bottom to top: 11576_8. 4990_10 = 11576_8 11576_8 Step 12: Convert 4990_10 to base 16. 4990 &÷ 16 = 311 \ remainder\ 14 \ (E), \\ 311 &÷ 16 = 19 \ remainder\ 7, \\ 19 &÷ 16 = 1 \ remainder\ 3, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 137E_16. 4990_10 = 137E_16 137E_16