Arithmetic Process in Computer Systems
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The document discusses arithmetic operations in digital computers. It describes how the arithmetic unit performs additions, subtractions, multiplications, and divisions by taking information from memory and processing it. It also explains how serial and parallel adders work to perform addition operations through shifting and adding bits. The document further discusses the complement technique for representing positive and negative numbers in binary, including using 1s and 0s to indicate sign and how to write numbers in signed and 2's complement form.
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- 1. Arithmetic Operations Ir. SNMP Simamora, MT. Laboratorium Sistem Komputasi & Jaringan Akses
- 2. Arithmetic Unit Operation The arithmetic unit of a digital computer contains the logic circuitry for performing additions, substractions, multiplications, and divisions Information to be processed by the computer is generally placed in memory first taken into the arithmetic unit at some later time
- 3. Computer Systems General Scheme
- 4. Arithmetic Unit Operation The arithmetic operations performed need only be those of addition and substraction Ex: 12 2 ÷
- 5. Serial Adder – simplified block diagram
- 6. Serial Adder – Data at start
- 7. Serial Adder – After first shift pulse
- 8. Serial Adder Input data is shift into the input register This input number can then be serially added to the Accumulator value stored in a second shift register; using one of the full adder circuits
- 9. Parallel Adder – logic diagram
- 10. Parallel Adder The logic circuitry is simpler, since only an add signal is required to obtain parallel addition. A Full Adder (FA) circuit is required for each bit position On an ADD instruction the data read into the MIR is added to that in the accumulator on CS5; the resulting sum being transferred into the AR.
- 11. Complement Technique Utilizing the 1 or 0 bit to specify the plus or minus sign This procedure specifically requires using 1 for negative sign and 0 for positive sign Positive numbers are written with the 0 sign in the most significant position with the positive absolute value
- 12. Complement Technique Negative numbers are written with the 1 sign in the ost significant position and the complement form of the number. Both number, positive and negative, should be written with equal digits and sufficient number to include the sum number without mixing up the sign with the number part.
- 13. Complement Technique Ex: -Write the following numbers in signed form: +7 +12 -3 -9 -20
- 14. Solution: sign sign 1 101100 1 101011 010100 – 20 1 110111 1 110110 001001 – 9 1 111101 1 111100 000011 – 3 0 001100 0 001100 001100 +12 0 001111 0 001111 001111 +7 Signed (2’s complement) Signed (1’s complement) Absolute magnitude Number
- 16. Ex: (00011001) 2 + (00010011) 2 = (…) 2 Solution:
- 17. Ex: (00011001) 2 - (00010011) 2 = (…) 2 Solution: