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Signed Integers (Cont.)

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Converting Signed Decimal to Hexadecimal

• Convert the absolute value of the decimal integer to hexadecimal.
• If the original decimal integer was negative, form the two’s complement of the hexadecimal number.

Starting value: (-1462)10	(-1462)10
Step 1: Convert the absolute value to hexadecimal
Step 2: Reverse the digits
Step 3: Add 1 to the value from Step 2	+	0	0	0	1
Step 4: Form the two’s complement
2’s complement notation of (-1462)10 is		( )16

Converting Signed Hexadecimal to Decimal

• If the highest bit is a 0, convert the unsigned hexadecimal integer to decimal.
• If the highest bit is a 1, it is stored in two’s complement notation.

Starting value: (8A20)16		8	A	2	0
Step 1: Reverse the digits
Step 2: Add 1 to the value from Step 1	+	0	0	0	1
Step 3: Form the two's complement
Step 4: Convert to decimal		negative ( )16 = ( )10

Maximum and Minimum Values
A signed integer of n bits uses only n-1 bits to represent its magnitude.

Storage Type	Maximum Values	Minimum Values
Signed byte	(01111111)2 = 27 – 1 = (127)10	(10000000)2 = -27 = (-128)10
Signed halfword	(0111111111111111)2 = 215 – 1 = (32,767)10	(1000000000000000)2 = -215 = (-32,768)10

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“A man is not called wise because he talks and talks again;           but if he is peaceful, loving and fearless then he is in truth called wise.”           ― Dhammapada, The Dhammapada: The Sayings of the Buddha