Question

[5] <§3.2> What is 5ED4 - 07A4 when these values represent unsigned 16-bit hexadecimal numbers? The result should be written in hexadecimal. Show your work.

Short answer

The required result will be 5730.

Step-by-step solution

Define the concept.

The hexadecimal number system uses base 16 where the decimal number system uses base 10 and the binary number system uses base 2.

For example, “A” is equivalent to the value of decimal number system “10” and that is also equivalent to the value of binary number system “1010”.

Determine the calculation.

Given, the two values 5ED4, 07A4 are represented in unsigned 16-bit hexadecimal numbers.

5ED4 is equivalent to the value of binary number system 0101 1110 1101 0100 and 07A4 is equivalent to the value of binary number system 0000 0111 1010 0100.

For the subtraction,

$$\begin{gathered} 0101111011010100 \\ -0000011110100100 \\ ---------------- \\ 0101011100110000 \\ 0101011100110000 \\ 5730 \end{gathered}$$

0101 0111 0011 0000 is equivalent to the value of hexadecimal number system 5730.

Hence,

$$\begin{gathered} 5ED4 \\ -07A4 \\ -------- \\ 5730 \end{gathered}$$

So, the required result is 5730 which is in hexadecimal.