Computer Arithmetic (Part 2)
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The document discusses integer representation in computers. It explains that integers are stored using binary and discusses two common methods: sign-magnitude and two's complement. It describes how positive and negative numbers are represented using each method and explains the benefits of two's complement representation, which includes only one representation of zero and simple arithmetic. The document also discusses the range of numbers that can be represented using 8-bit and 16-bit two's complement and how negation is performed in two's complement.
Computer Arithmetic (Part 2)
- 1. Organisasi dan Arsitektur Komputer Ajeng Savitri Puspaningrum, M.Kom Pertemuan 12
- 3. Learning computer arithmetic Learning integer representation
- 4. Integer Representation Only have 0 & 1 to represent everything Positive numbers stored in binary e.g. 41=00101001 No minus sign Sign-Magnitude Two’s complement
- 5. Sign-Magnitude Left most bit is sign bit 0 means positive 1 means negative +18 = 00010010 -18 = 10010010 Problems Need to consider both sign and magnitude in arithmetic Two representations of zero (+0 and -0)
- 6. Two’s Complement +3 = 00000011 +2 = 00000010 +1 = 00000001 +0 = 00000000 -1 = 11111111 -2 = 11111110 -3 = 11111101
- 7. Range of Numbers 8 bit 2s compliment +127 = 01111111 = 27 -1 -128 = 10000000 = -27 16 bit 2s compliment +32767 = 011111111 11111111 = 215 - 1 -32768 = 100000000 00000000 = -215
- 8. Benefits One representation of zero Arithmetic works easily (see later) Negating is fairly easy 3 = 00000011 Boolean complement gives 11111100 Add 1 to LSB 11111101 * LSB : Least significant bit
- 9. Negation Special Case 1 0 = 00000000 Bitwise not 11111111 Add 1 to LSB +1 Result 1 00000000 Overflow is ignored, so: - 0 = 0
- 10. Negation Special Case 2 -128 = 10000000 bitwise not 01111111 Add 1 to LSB +1 Result 10000000 So: -(-128) = -128 Monitor MSB (sign bit) It should change during negation
- 11. Refference Stalling, William, Computer Organization and Architecture, 10th Edition, Pearson, 2015 Abdurohman, Maman, Organisasi dan Arsitektur Komputer revisi ke-4, Penerbit Informatika, 2017