Binary Multiplication

Question 1

What are the two numbers in a multiplication called? Which is which?

Answer 1

> Multiplicand = Number to be multiplied

> Multiplier = Number to multiply the multiplicand by

Question 2

What is the table for single digit multiplication?

Answer 2

x | 0 | 1 |
0 | 0 | 0 |
1 | 0 | 1 |

Question 3

How can single digit multiplication be implamented?

Answer 3

Using an AND gate

Question 4

For two multiplied binary numebrs what is the total number of bits required for any result?

Answer 4

Max Width = n + m

Question 5

How can two unsigned binary numbers be multiplied?

Answer 5

Using binary long multiplication

Question 6

How can two signed binary number be multiplied?

Answer 6

By using binary long multiplication but we extend to inifinity the most significant bit of each binary number and then take the max width number of bits from the result

Question 7

What is a shift add multiplier?

Answer 7

This method uses an ALU and shoft registers with an output register and some control logic to calculate the total

Question 8

What is the benefit and draw back of using a shift add multiplier?

Answer 8

> Good: because it uses few added logic elements to implament
Bad: Because it takes a lot of clock cycles to calcualte

Question 9

What are the 4 differet registers used in a shift add multiplier?

Answer 9

> Register I: Counter (for number of clock cycles)
Register B: Multiplicand
Register Q: Multiplier
Register A: Output

Question 10

What is the process for shift add multiplication?

Answer 10

1. Output register A = 0
   [LOOP]
2. Read the register Q to see if it has a 1 in its first position
   > If it is a 1 then add B to A using the ALU
3. The output is then fed back into the input of the ALU
4. Register B is then left shifted
5. Register Q is then right shifted
   [GOTO LOOP]
   > The process repeats until the I register is equal to the number of digits in the Q register
   > Final output A is the total

Question 11

What is an array multiplier?

Answer 11

This is a method of conducting a multiplication in a signle clock cycle using hardware

Question 12

What is a 1-bit array multiplier?

Answer 12

An AND gate

Question 13

What is the circuit for a 4-bit array multiplier?

Answer 13

[Picture5]

Question 14

What are the pros and cons of array multipliers?

Answer 14

Pros: It can perform unsigned multiplication in a single clock cycle
Cons:
> Propagation delay can limit speed
> Lots of resources required
> Takes up a lot of space