Microprocessor and Computer Architecture · Unit 5
Fixed Point Arithmetic Algorithms
Exam-focused notes for Fixed Point Arithmetic Algorithms (Microprocessor and Computer Architecture, BIT151): what the TU syllabus asks and how it has actually been tested, with 7 solved past questions from this unit.
What this unit covers
- Booths multiplication algorithm
- Restoring division algorithm
- Binary division process and step by step execution
- Multiplication and division hardware implementation
Booths multiplication algorithm
Explain the working procedure of Booth Multiplication algorithm. [5]
Booth's algorithm is an efficient algorithm for multiplying two signed binary numbers represented in 2's complement form. It handles both positive and negative numbers uniformly and reduces the number of additions/subtractions required. --- Component Descri...
Full solved answer →Perform 2's complement multiplication of (15) x (-13) using Booth's Multiplication algorithm. [5]
- Multiplicand = 15 - Multiplier = −13 - Method: Booth's algorithm, 2's complement We need enough bits to represent both operands and their negatives in 2's complement. - $+15 = 01111$ needs 5 bits, but $+15$ in signed form requires a leading 0, so minimum ...
Full solved answer →Perform multiplication of (-9) x (-13) using Booth’s Multiplication algorithm. [5]
- Multiplicand $M = -9$ - Multiplier $Q = -13$ - Expected product $= (-9)(-13) = +117$ $+9 = 01001 \Rightarrow -9 = 10111$ (2's complement) $+13 = 01101 \Rightarrow -13 = 10011$ (2's complement) So: - $M = 10111$ - $-M = 01001$ - $Q = 10011$ - $Q{-1} = 0$ -...
Full solved answer →Restoring division algorithm
Show the step-by-step division process using Restoring Division Algorithm of 194 ÷\div÷ 10) (AQ= 10100011 by B=1011). [5]
- Combined register AQ = 10100011 (8 bits) - Divisor B = 1011 (4 bits) = 11 in decimal - Split: A (accumulator) = 1010, Q (dividend/quotient) = 0011 Interpretation check: The title says "194 ÷ 10". Note that $101000112 = 163$, not 194, and $10112 = 11$, not...
Full solved answer →State an algorithm for the restoring division method of fixed point binary division.Show the step-by step division process using restoring division algorithm when 448(0111000000) is divided by 17(10001). Use 5-bit register to represent the numbers.[10]
Registers: A (accumulator/partial remainder), Q (holds dividend, then quotient), M (divisor), Count = number of bits. 1. Initialize: A = 0, Q = dividend, M = divisor, Count = n. 2. Repeat n times: - Shift the combined register (A, Q) left by 1 bit. - A = A ...
Full solved answer →Write a program to perform 8 bit division of data stored in memory location 8050 by data stored in memory location 8051 and store the quotient in memory location 8052 and remainder in 8053 memory location. [5]
- Dividend: stored at memory location 8050H - Divisor: stored at memory location 8051H - Quotient: store at memory location 8052H - Remainder: store at memory location 8053H --- The 8085 microprocessor does not have a direct division instruction. Division i...
Full solved answer →Multiplication and division hardware implementation
Write a program to perform 8 bit multiplication in 8085 processor. (Assume data and memory yourself). [5]
The problem says "Assume data and memory yourself," so I choose: Item Value Memory Location ------------------------------ Multiplicand 05H 2200H Multiplier 04H 2201H Result low byte (computed) 2202H Result high byte (computed) 2203H No mandatory numeric in...
Full solved answer →Make Unit 5 stick
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