Page 1034 - The Mechatronics Handbook

TABLE 36.2 Arithmetic Operations
Algebraic Form Arithmetic Form
Augend
+ Addend
Addition Sum = Augend + A ddend
Sum
Minuend
− Subtrahend
Subtraction Difference = Minuend − Subtrahend
Difference
Multiplicand
×Multiplier
Multiplication Product = Multiplicand × Multiplier
Product
Quotient Remainder
Division Dividend/Divisor = Quotient
+ Remainder/Divisor Divisor Dividend

TABLE 36.3 Single Digit Binary Arithmetic Table

(a) Addition (b) Multiplication
0 1 0 1
00 1 00 0
11 10 10 1

TABLE 36.4 Binary Arithmetic Operation Examples
Addition: Multiplication:
1 1 0 0 carries 1 1 0 1 multiplicand
1 1 1 0 0 augend ×1 1 0 multiplier
+ 1 1 0 1 addend 0 0 0 0 partial product 1
1 0 1 0 0 1 sum 1 1 0 1 partial product 2
1 1 0 1 partial product 3
1 0 0 1 1 1 0 product
Subtraction, borrow method: Division, with fraction remainder:
remainder
10 borrows 1 1 1
1 0 1 minuend quotient 1 0 1 1
1 0 0 1 0
− 1 0 subtrahend
1 1 difference 1 0 1 1 1 1 0 0 1 1 0 1 dividend
divisor 1 0 1 1
0 1 1 1 0
1 0 1 1
0 1 1 1
Subtraction, payback method: Division, with remainder in quotient:
quotient
10 borrows
1 0 1 minuend .1 0 1 0 0 0 1 ...
1 0 1 1 1 1 1.0 0 0 0 0 0 0
− 1 payback divisor dividend
1 0 1 1
− 1 0 subtrahend 1 1 0 0
difference
1 1
1 0 1 1
0 1 0 0 0 0
1 0 1 1
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