Binary Multiplication Repeated Left-shift and Add 4-bit Multiplier Circuit Repeated Add and Right-shift Binary Division Repeated Right-shift and Subtract Repeated Subtract and Left-shift

1. Digital Design – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com

2. Digital Design – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 2
Session 5: Focus
 Binary Multiplication
◦ Repeated Left-shift and Add
 4-bit Multiplier Circuit
◦ Repeated Add and Right-shift
 Binary Division
◦ Repeated Right-shift and Subtract
◦ Repeated Subtract and Left-shift

3. Digital Design – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
Binary Multiplication Algorithms

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Basic Rules of Multiplication
 Basic rules of multiplication of two bits are given
below:
Which logic gate, does this output
look similar to?

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Repeated Left-Shift and Add
 Let us look at a multiplication algorithm: Repeated Left-Shift and
Add
◦ Left-Shift the multiplicand and add
 Each bit of the multiplier determines whether a 0 is added
or a shifted version of the multiplicand
◦ 0 implies zero is added, 1 implies shifted multiplicand is added
……….. (138)10
Left-Shift by 1 bit

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4-bit Multiplier Circuit – Left Shift and Add
 The circuit blocks that are needed for the 4-bit multiplier are:
◦ An 8-bit Shift register
◦ An 8-bit adder
◦ An 8-bit D-type register to hold the product
◦ Some control circuitry
 They will all be studied during later part of this course

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Repeated Add and Right-Shift
Right-shiftedbyonebit
23
6
138
x
Result: 10001010

8. Digital Design – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com
Binary Division Algorithms

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Binary Division
 While binary multiplication is the process of repeated
addition
◦ Binary division is the process of repeated subtraction
 Binary division can be performed by using either
◦ The ‘repeated right-shift and subtract’ or
◦ The ‘repeated subtract and left-shift’ algorithm

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Repeated Right-Shift and Subtract
 Let us look at a division algorithm: Repeated Right-
Shift and Subtract 38
12 Reminder = 2
Quotient = 3
(38)
(12)
If part of dividend is lower than divisor,
No subtraction is performed

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Repeated Subtract and Left-Shift
 Let us look at a division algorithm: Repeated Subtract
and Left-Shift
38
12 Reminder = 2
Quotient = 3
(38)

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Session 5: Summary
 Binary Multiplication
◦ Repeated Left-shift and Add
 4-bit Multiplier Circuit
◦ Repeated Add and Right-shift
 Binary Division
◦ Repeated Right-shift and Subtract
◦ Repeated Subtract and Left-shift

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References
Ref 1 Ref 2