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The example on page 190 of the textbook shows the restoring division of dividing 7 by 2. Redo the same example by now dividing 15 by 2. Confirm that the quotient is 7 and the remainder is 1 at the end of the algorithm's execution.

The example on page 190 of the textbook shows the restoring division of dividing 7 by 2. Redo the same example by now dividing 15 by 2. Confirm that the quotient is 7 and the remainder is 1 at the end of the algorithm's execution.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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The example on page 190 of the textbook shows the restoring division of dividing 7 by 2. Redo the same example by now dividing 15 by 2. Confirm that the quotient is 7 and the remainder is 1 at the end of the algorithm's execution.

Write down the answer similar to the table in Figure 3.10 page 192 of the textbook.

A Divide Algorithm EXAMPLE Using a 4-bit version of the algorithm to save pages, leť's try dividing 7 by2. or 0000 0111 by 0010, ten two two Figure 3.10 shows the value of each register for each of the steps, with the quotient being 3 and the remainder 1 Notice that the test in step 2 of whether the remainder is positive or negative simply tests whether the sign bit of the Remainder register is a 0 or 1. The surprising requirement of this algorithm s that it takes n +1 steps to get the proper quotient and remainder. ANSWER ten ten
Transcribed Image Text:A Divide Algorithm EXAMPLE Using a 4-bit version of the algorithm to save pages, leť's try dividing 7 by2. or 0000 0111 by 0010, ten two two Figure 3.10 shows the value of each register for each of the steps, with the quotient being 3 and the remainder 1 Notice that the test in step 2 of whether the remainder is positive or negative simply tests whether the sign bit of the Remainder register is a 0 or 1. The surprising requirement of this algorithm s that it takes n +1 steps to get the proper quotient and remainder. ANSWER ten ten
F9 F10 F11 E12 PrtSca Chapter 3 Arithmetic for Computers Divisor Remainder Quotient 00000111 0110 0111 to 000111 Step 0010 0000 Iteration to 00 0010 0000 Initial values 0000 0. 0010 0000 1: Rem = Rem - Div %3D 0000 2b: Rem < 0 +Div, sll Q, QO = 0 3: Shift Div right to01 0000 t0000111 to00 111 0111 to 000111 0001 0000 to 00 1: Rem = Rem - Div t001 0000 %3D to 00 2b: Rem < 0 +Div, sll Q, Q0 = 0 3: Shift Div right to 00 1000 00000111 to 00 to 00 to 00 1000 0111 1111 1: Rem = Rem - Div to00 1000 to00 0111 to 00 2b: Rem < 0= +Div, sll Q, Q0 = 0 3: Shift Div right %3D to 00 to 000100 to 000111 to 00 to000100 O000 0011 1: Rem Rem - Div %3D t001 to00 0100 to000011 2a: Rem 20 = sll Q, Q0 = 1 3: Shift Div right 4 to 000010 to 000010 0o 000011 O000 0001 t001 t001 1: Rem = Rem- Div 0011 to000010 to000001 2a: Rem 20 = sll Q, Q0 = 1 3: Shift Div right 0011 to 000001 to000001 IGURE 3.10 Division example using the algorithm in Figure 3.9. The bit examined to determine e next step is circled in color. 1. 2. 3.
Transcribed Image Text:F9 F10 F11 E12 PrtSca Chapter 3 Arithmetic for Computers Divisor Remainder Quotient 00000111 0110 0111 to 000111 Step 0010 0000 Iteration to 00 0010 0000 Initial values 0000 0. 0010 0000 1: Rem = Rem - Div %3D 0000 2b: Rem < 0 +Div, sll Q, QO = 0 3: Shift Div right to01 0000 t0000111 to00 111 0111 to 000111 0001 0000 to 00 1: Rem = Rem - Div t001 0000 %3D to 00 2b: Rem < 0 +Div, sll Q, Q0 = 0 3: Shift Div right to 00 1000 00000111 to 00 to 00 to 00 1000 0111 1111 1: Rem = Rem - Div to00 1000 to00 0111 to 00 2b: Rem < 0= +Div, sll Q, Q0 = 0 3: Shift Div right %3D to 00 to 000100 to 000111 to 00 to000100 O000 0011 1: Rem Rem - Div %3D t001 to00 0100 to000011 2a: Rem 20 = sll Q, Q0 = 1 3: Shift Div right 4 to 000010 to 000010 0o 000011 O000 0001 t001 t001 1: Rem = Rem- Div 0011 to000010 to000001 2a: Rem 20 = sll Q, Q0 = 1 3: Shift Div right 0011 to 000001 to000001 IGURE 3.10 Division example using the algorithm in Figure 3.9. The bit examined to determine e next step is circled in color. 1. 2. 3.
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