Numeral Systems

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Numeral Systems
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• Instructions in SPARC occupy 32 bits
• 8 bits to specify the instruction
• 5 bits for address of registers
• 1 bits to specify if there is a second source
  register or an immediate constant
• 8 bits to either specify second source register
  or to provide an additional 8 bits to specify
  floating point instructions
• 32 bits of instruction can be written as
  hexadecimal constant numbers 0x902765ab

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Instructions

• Format three
• Majority of instructions
• Format one
• Call instruction
• Format two
• Branch instructions

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• What should you know?

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• Numeral
• A symbol or group of symbols that represent a
  number.
• Different numerals 11, eleven, XI
• Numeral System
• Framework where a set of numbers are represented
  in a consistent manner.
• Numeral 11
• Binary numeral for three
• Decimal numeral for eleven
• .

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Different bases

• In computing
• Basis of digital computers base 2
• Modern computers
• Transistors
• High or low voltage
• Bit
• The smallest unit of memory for 2 different
  voltage
• Bits are arranged in groups
• Processing
• Shorter binary numbers
• More manageable for human

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Numeral systems

• Hexadecimal
• Numeral system with base 16
• Use symbols 0-9, a-f, or A-F
• One hexadecimal digit stands in place of four
  binary digits.

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conversion

• X Bin Dec
• 0 0000 0
• 1 0001 1
• 2 0010 2
• 3 0011 3
• 4 0100 4
• 5 0101 5
• 6 0110 6
• 7 0111 7
• 8 1000 8
• 9 1001 9
• A 1010 10
• B 1011 11
• C 1100 12
• D 1101 13
• E 1110 14
• F 1111 15

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Binary to Hexadecimal

• Example 1. convert Binary to Hexadecimal
• STEP 1. Break the Byte into 'quartets'
• STEP 2. covert each quartet to its Hex equivalent
  
• You need to know how to convert decimal to binary
  and the other way around.

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Binary to Decimal

• Step1. start from the first digit from right, and
  set the digit counter to 0
• Step 2. Multiply the current digit by 2 to the
  power of the digit counter
• Step 3. Add the result to SUM
• Step 4. get the next digit , set the digit
  counter and jump to Step 2.

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Binary to Hexadecimal

• Example 1. Consider Binary 1000100100110111  (a
  16-bit Byte)
• STEP 1 Break the Byte into 'quartets' -  1000 
  1001  0011  0111
• STEP 2 covert each quartet to its Hex equivalent
  -  8937
• Therefore ... 1000100100110111 8937Hex

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Binary to Hexadecimal

• Example 2. Consider Binary 1111110001000001
• STEP 1 Break the Byte into 'quartets' - 1111 
  1100  0100 0001
• STEP 2 Use the table above to covert each quartet
  to its Hex equivalent -  FC41
• Therefore ... 1111110001000001 FC41Hex

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Binary to Hexadecimal

• Example 3. Consider Binary 11010101STEP 1 Break
  the Byte into 'quartets' - 1101  0101
• STEP 2 Use the table above to covert each quartet
  to its Hex equivalent -  D5
• Therefore ... 11010101 D5Hex