Lesson -5 Binary Arithmetic (1).pdffngmh

Mindanao Polytechnic College GSC
Mindanao Polytechnic College
General Santos City
Binary Arithmetic
Narene M. Nagares, MIT
Department of Information Technology

Binary Arithmetic
• Arithmetic operations in digital systems are
usually done in binary because design of logic
circuits to perform binary arithmetic is much
easier than for decimal.
• Binary arithmetic is carried out in much the
same manner as decimal, expect with the
addition and multiplication tables are much
simpler.
COMP1 - Computer Fundamentals & Programming 2

Binary Addition
• Addition table for binary numbers:
and carry 1 to the next column
Simple explanation why there is a
carry 1:
• When you do 1+1, the result in
decimal is 2, the binary number of
2 is 1 0, that is 2 bits.
• The 0 is written down and the 1 is
carried to the next column.
+

Binary Addition
• Example:
+
Adding three 1’s is equivalent to
1 1 in binary or 3 in decimal.
Breakdown:
1
+ 1
1 0
+ 1
1 1

Binary Addition
• Another Example:
*You may convert it in decimal
to check if your answer is correct.

Binary Subtraction
• Subtraction table for binary numbers:
and borrow 1 from the next column
When zero borrows 1 from the next
column, zero does not become 1, rather,
it becomes 1 0, the binary number of
decimal number 2. When you subtract 1
from 2, the result is 1.

Binary Subtraction
• Examples:
• Keep borrowing from
the next column until
you are able to find
the value 1.
• (1 0) represents the
number 2 in decimal .
When the previous
column borrows, the
value from the current
column becomes 1.
This becomes:
1 0
And 1 0 – 1 = 1.

Binary Multiplication
• The multiplication table for binary numbers:

• Example: Multiplication of 1310 by 1110 in
binary:

• To avoid carries greater than 1, you may add
partial products one at a time:

Binary Division
• Binary division is similar to decimal division,
except it is much easier because the only two
possible quotient digits are 0 and 1.

Binary Division
• Example: Division of 14510 by 1110 in binary:
• If we start comparing the divisor (1011) with the upper
four bits of the dividend (1001), we find that we cannot
subtract without a negative result, so we move the
divisor one place to the right and try again.
–

Binary Division
• This time we can subtract 1011 from 10010 to give 111
as a result, so we put the first quotient bit of 1 above
10010. We then bring down the next dividend bit (0) to
get 1110 and shift the divisor right.
–

• We then subtract 1011 from 1110 to get 11,
so the second quotient is 1.
Binary Division
–

• When we bring down the next dividend bit,
the result is 110, and we cannot subtract the
shifted divisor, so the third quotient is 0.
Binary Division
–

• We then bring down the last dividend bit and subtract 1011 from
1101 to get a final remainder of 10, and the last quotient bit is 1.
Binary Division
–
–
*The quotient is
1101 with a remainder of 10.

Exercises (Show your solution)
1. Add, subtract, and multiply in binary:
(a) 1111 and 1010
(b) 110110 and 11101
(c) 100100 and 10110
2. Divide in binary:
(a) 11101001 ÷ 101
(b) 1110010 ÷ 1001
Check your answers by multiplying out in binary and
adding the remainder.

Lesson -5 Binary Arithmetic (1).pdffngmh

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