Questions: Perform the subtraction. EFC16-9516 EFC16-9 B 516=square16 (Simplify your answer.)

Perform the subtraction. EFC16-9516 EFC16-9 B 516=square16 (Simplify your answer.)
Transcript text: Perform the subtraction. \[ \begin{array}{c} \mathrm{EFC}_{16}-95_{16} \\ \mathrm{EFC}_{16}-9 B 5_{16}=\square_{16} \end{array} \] (Simplify your answer.)
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Solution

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Solution Steps

To perform the subtraction of numbers in base 16 (hexadecimal), we first convert the hexadecimal numbers to decimal, perform the subtraction in decimal, and then convert the result back to hexadecimal.

Step 1: Convert Hexadecimal to Decimal

To perform the subtraction, we first convert the hexadecimal numbers to decimal. The hexadecimal number \(\text{EFC}_{16}\) converts to decimal as \(3836\), \(\text{95}_{16}\) converts to \(149\), and \(\text{9B5}_{16}\) converts to \(2485\).

Step 2: Perform Subtraction in Decimal

Next, we perform the subtraction in decimal:

  • \(3836 - 149 = 3687\)
  • \(3836 - 2485 = 1351\)
Step 3: Convert Decimal Result Back to Hexadecimal

Finally, we convert the decimal results back to hexadecimal:

  • \(3687\) in decimal is \(\text{E67}_{16}\)
  • \(1351\) in decimal is \(\text{547}_{16}\)

Final Answer

The results of the subtractions are:

  • \(\text{EFC}_{16} - \text{95}_{16} = \boxed{\text{E67}_{16}}\)
  • \(\text{EFC}_{16} - \text{9B5}_{16} = \boxed{\text{547}_{16}}\)
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