1. Data
Binary Arithmetic

2. Binary Addition
The process of performing addition in binary is very similar to addition in denary. 1 + 1 + 1 +
Rules:
0 -
0 + 1 = 1
1 + 1 = 0 carry 1
= 1 carry 1
Question:
What is ?
Complete tasks 4.1 and 4.2.

3. Overflow
When there isn’t enough room for a result, this is called an overflow and it produces an overflow error. 1 +
No room for a carry, so it is lost and we get the wrong answer.
Humans can easily work around this, but it isn’t so easy for a computer.

4. Binary Subtraction
The process of performing subtraction in binary is very similar to subtraction in denary. 1 - 10 1 - 1 -
Rule:
0 - 1 won’t go so borrow 10 (2) from the column to the left = 1.
Question:
What is ?
Complete tasks 4.3 and 4.4.

5. 1 = minus 0 = plus Sign and Magnitude
This is the simplest method of representing negative numbers in binary. The most significant bit is the ‘sign bit’.
1 = minus = plus
Sign bit
128 64 32 16 8 4 2 1
+27
-27
Question:
Convert this sign and magnitude binary number to denary: 1111
Complete tasks 4.5 and 4.6.

6. The Problem with Sign and Magnitude
The problem with sign and magnitude is that addition doesn’t always work. 1
(+7)
(-5) +
(-12)

7. -128 + 8 + 4 + 1 = -115 Two’s Complement
Two’s complement is an alternative method of representing negative numbers. This method works with binary addition.
The most significant bit is a minus number.
-128 64 32 16 8 4 2 1
= -115
Question:
Convert this sign and magnitude binary number to denary: 1101
Complete tasks 4.7 and 4.8.

8. Floating Point Numbers
In binary floating point numbers are split into two parts; the Mantissa and the Exponent.
Mantissa
Exponent
The mantissa contains the actual number and the exponent defines the position of the binary point.

9. Floating Point Numbers
The numbers to the right of the binary point define the fraction.
1/ / /8 1/16
8/16 4/16 2/16 1/16
In denary the number above is:
7 ½
Complete task 4.9.