Final answer:
To sum the numbers 75 and 46 in 8-bit signed magnitude arithmetic, convert them to binary signed magnitude, sum the binary values neglecting the sign bit (0 for positive), and the result is 01111001, which corresponds to the decimal number 121. This matches the direct decimal addition of 75 and 46, which also equals 121.
Step-by-step explanation:
To find the sum of the decimal numbers 75 and 46 using 8-bit signed magnitude arithmetic, we first need to convert these numbers into their binary signed magnitude equivalents. The number 75 in binary is 01001011 and the number 46 is 00101110. When we add these two binary numbers together, we neglect the sign bit and add the remaining bits.
01001011 (This is 75 in binary signed magnitude)
+00101110 (This is 46 in binary signed magnitude)
=01111001
The leftmost bit is the sign bit (0 for positive numbers). The remaining bits represent the number 121 in binary, which is the sum of 75 and 46. To verify our answer in decimal, we can simply add the two original numbers together: 75 + 46 = 121, which confirms that our binary addition is correct.