Mathematics with Binary

QuestionBelow is a binary string

Which is the least significant bit (LSB)? Which is the most significant bit (MSB)?

0 0 0 1 0 1 1 1

MSB LSB

ObjectivesAdd two binary numbers and multiply two

binary numbers.

Convert a denary integer into Two's Complement and vice versa.

Describe the use of Two's Complement to perform subtraction.

Binary AdditionYou have to be able to add together two

binary numbers, and it’s easy!

Lets try to add together 00011001 00011010

Rules for Maths in Binary

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10 (carry 1)

1 + 1 + 1 = 11(1 and carry 1)

0001100100011010

110011

1100

Binary Subtraction Subtraction has an extra step as we have to use two’s

complement, to make the number that we are taking way into a negative

Two’s Complement is used to convert a number to a negative

Lets look at taking away the following: 00010001 (17) 00001101 (13 – Decimal)

Step 1 – Convert 13 to twos complement

11110011Step 2 – We now add together the two numbers

1111001100010001

00100000

111111

Rules for Maths in Binary

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10 (carry 1)

1 + 1 + 1 = 11(1 and carry 1)

Binary Multiplication This can be slightly longer but follows the same rules as

doing multiplication in denary.

Lets look at multiplying the following numbers: 10110 00101

1011000101 Rules for

Multiplication

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

10110

10110. . . . .

. . . . .. . . . .

1101110

1