Andrew H. Fagg: Embedded Real-
Time Systems: Binary Arithmetic 2
Today
• Binary addition
• Representing negative numbers
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• Binary addition • Representing negative numbers, Exams of Number Theory
One oddity: we can represent one more negative number than we can positive numbers Page 42 Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic 55 ...
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Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Today
- Binary addition• Representing negative numbers
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
Consider the following binary numbers:
How do we add these numbers?
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
And we have a carry now!
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
0 0 1And we have a carry again!
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
One more carry!
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Binary Addition
Behaves just like addition in decimal, but:• We carry to the next digit any time the sum
of the digits is 2 (decimal) or greater
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Negative Numbers
So far we have only talked about
representing non-negative integers
- What can we add to our binary
representation that will allow this?
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude Representation+
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude Representation+
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude RepresentationWhat is the problem with this approach?• Some of the arithmetic operators that we
have already developed do not do the rightthing
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude RepresentationOperator problems:• For example, we have already designed a
counter (that implements an ‘increment’operation)
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude RepresentationOperator problems:-
Increment
Andrew H. Fagg: Embedded Real-Time Systems: Binary Arithmetic
Sign Magnitude RepresentationOperator problems:-
Increment