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Hexadecimal notation is a convenient way to represent binary numbers, using fewer digits and minimizing error risks. When converting from hexadecimal to decimal, especially for 2's complement binary representation, it's essential to determine the sign of the number first. If the most significant hex digit is 8 or greater, the number is negative. For example, converting 6F from hex to decimal results in a positive 111 decimal, while A0F yields -1,521 after applying 2's complement. This process illustrates the importance of understanding number representations in computing.
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Hexadecimal Notation • It is often convenient to write binary (base-2) numbersas hexadecimal (base-16) numbers instead. • fewer digits -- four bits per hex digit • less error prone -- easy to corrupt long string of 1’s and 0’s
Convert Hexadecimal (2’s C binary) to Decimal • Given a hex digit that represents 2’s complement binary, convert into a decimal. • Example: 6Fhex or x6F • Determine the sign of the number. If the msh (most significant hex) value is 8 or greater then the sign is negative.6Fhex, sign + b/c msh (6) < 8sign positive • Use positional notation to convert6x161 + Fx160 = 6x161 + 15 = 96 + 15 = 1116Fhex = 111ten
Convert Hexadecimal (2’s C binary) to Decimal • Given a hex digit that represents 2’s complement binary, convert into a decimal. • Example: A0Fhex or xA0F • Determine the sign of the number. If the msh (most significant hex) value is 8 or greater then the sign is negative.A0Fhex, sign - b/c msh (A) < 8sign negative • Since negative, must apply 2’s complement • Convert to signed magnitude to decimal with positional notation-(5x162 + Fx161 + 1x160) = -(5x256 + 15x16 + 1) = -1,521 5F0+ 1 5F1 FFF- A0F 5F0 A0F= - 5F1
