Task Two

1. Convert the following decimal numbers to binary and then to hexadecimal:

a. 157

• Decimal to Binary: Divide by 2 and track remainders:

  • $157÷2=78$ remainder 1
  • $78÷2=39$ 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

  So, $157$ in binary is 10011101.

• Binary to Hexadecimal: Group binary digits in sets of 4 (from right):

  • 1001 1101 = 9D in hexadecimal.

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b. 365

• Decimal to Binary:

  • $365÷2=182$ remainder 1
  • $182÷2=91$ remainder 0
  • $91÷2=45$ remainder 1
  • $45÷2=22$ remainder 1
  • $22÷2=11$ remainder 0
  • $11÷2=5$ remainder 1
  • $5÷2=2$ remainder 1
  • $2÷2=1$ remainder 0
  • $1÷2=0$ remainder 1

  So, $365$ in binary is 101101101.

• Binary to Hexadecimal:

  • Pad binary: 0001 0110 1101 = 16D in hexadecimal.

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c. 1023

• Decimal to Binary: $1023$ in binary is 1111111111.
• Binary to Hexadecimal: Group binary digits in sets of 4: 11 1111 1111 = 3FF in hexadecimal.

2. Convert the following hexadecimal numbers to binary and then to decimal:

a. 3F

• Hexadecimal to Binary: 3F = 0011 1111
• Binary to Decimal: $3F$ is $3\times 16+15=63$ in decimal.

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b. C7A

• Hexadecimal to Binary: C7A = 1100 0111 1010
• Binary to Decimal: $C7A$ is $12\times 256+7\times 16+10=3194$ in decimal.

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c. 4B2

• Hexadecimal to Binary: 4B2 = 0100 1011 0010
• Binary to Decimal: $4B2$ is $4\times 256+11\times 16+2=1202$ in decimal.

3. Convert the following octal numbers to binary and then to decimal:

a. 127

• Octal to Binary: 127 = 001 010 111
• Binary to Decimal: 001010111 = 87 in decimal.

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b. 345

• Octal to Binary: 345 = 011 100 101
• Binary to Decimal: 011100101 = 229 in decimal.

4. Given the binary number 11100110, convert it to octal and then to hexadecimal.

• Binary to Octal: Group in sets of 3: 111 001 110 = 716 in octal.
• Binary to Hexadecimal: Group in sets of 4: 1110 0110 = E6 in hexadecimal.

5. Convert the following decimal numbers to octal, then to binary, and finally to hexadecimal:

a. 145

• Decimal to Octal: $145$ in octal is 221.
• Octal to Binary: 221 in binary is 010 010 001.
• Binary to Hexadecimal: 01001001 = 91 in hexadecimal.

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b. 511

• Decimal to Octal: $511$ in octal is 777.
• Octal to Binary: 777 in binary is 111 111 111.
• Binary to Hexadecimal: 11111111 = FF in hexadecimal.

6. Convert the binary number 101101001 to octal and then to decimal.

• Binary to Octal: Group in sets of 3: 101 101 001 = 551 in octal.
• Binary to Decimal: $101101001$ is $361$ in decimal.

7. Show the steps for converting the decimal number 250 to binary and then to hexadecimal.

• Decimal to Binary: $250$ in binary is 11111010.
• Binary to Hexadecimal: 1111 1010 = FA in hexadecimal.

8. If you have the binary number 11101100, explain how you would convert it to octal and then to decimal.

• Binary to Octal: Group in sets of 3: 111 011 100 = 734 in octal.
• Binary to Decimal: $11101100$ is $236$ in decimal.

9. Explain the steps to convert the octal number 63 to hexadecimal.

• Octal to Binary: 63 in binary is 110 011.
• Binary to Hexadecimal: Group in sets of 4: 1100 11 = 33 in hexadecimal.

10. If you have the octal number 375, first convert it to decimal and then to hexadecimal.

• Octal to Decimal: $375$ in decimal is $3\times 64+7\times 8+5=253$.
• Decimal to Hexadecimal: $253$ in hexadecimal is FD.

11. Convert the octal number 1000 to hexadecimal and explain your process.

• Octal to Binary: 1000 in binary is 001 000 000 000.
• Binary to Hexadecimal: 0010 0000 0000 = 200 in hexadecimal.