Digital Electronics

1. REPRESENTATION
OF
BINARY NUMBERS
T.SRIKRISHNA

2. Representation of Binary Numbers:
• Binary numbers can be represented in signed
and unsigned way.
• Unsigned binary numbers do not have sign bit.
• Whereas signed binary numbers uses signed
bit as well as these can be distinguishable
between positive and negative numbers
T.Srikrishna, M.Sc, M.Tech. GVP

3. T.Srikrishna, M.Sc, M.Tech. GVP

4. 1. Unsigned Numbers:
• Unsigned numbers don’t have any sign, these can
contain only magnitude of the number.
Representation of Unsigned Binary Numbers:
• Since there is no sign bit in this unsigned binary
number, so N bit binary number represent its
magnitude only.
• Zero (0) is also unsigned number. This representation
has only one zero (0), which is always positive.
• Example-1: Represent decimal number 92 in unsigned
binary number.
(92)10= (1011100)2
• It’s 7 bit binary magnitude of the decimal number 92.
T.Srikrishna, M.Sc, M.Tech. GVP

5. 2. Signed Numbers:
• Signed numbers contain sign flag, this
representation distinguish positive and
negative numbers. This technique contains
both sign bit and magnitude of a number.
• (a) Signed Magnitude Method.
• (b) 1’s Complement Method.
• (c) 2’s Complement Method.
T.Srikrishna, M.Sc, M.Tech. GVP

6. 2.(a)Signed Magnitude Method
• In this method, number is divided into two
parts: Sign bit and Magnitude.
• If the number is positive then sign bit will be 0
and if number is negative then sign bit will be 1.
• Example: Let we are using 5 bits register. The
representation of -5 to +5 will be as follows:
T.Srikrishna, M.Sc, M.Tech. GVP

7. • The drawback of this system is that 0 has two
different representation
• one is -0 (e.g., 1 0000 in five bit register) and
second is +0 (e.g., 0 0000 in five bit register).
T.Srikrishna, M.Sc, M.Tech. GVP

8. 2.(b) 1’s Complement Method
• Positive numbers are represented in the same
way as they are represented in sign magnitude
method.
• If the number is negative then it is represented
using 1’s complement. First represent the number
with positive sign and then take 1’s complement
of that number.
1's complement
• The 1's complement of a number is found by
changing all 1's to 0's and all 0's to 1's. This is
called as taking complement or 1's complement.
T.Srikrishna, M.Sc, M.Tech. GVP

9. • Example of 1's Complement is as follows.
T.Srikrishna, M.Sc, M.Tech. GVP

10. • Example: Let we are using 5 bits register. The
representation of -5 and +5 will be as follows:
T.Srikrishna, M.Sc, M.Tech. GVP

11. • +5 is represented as it is represented in sign
magnitude method.
• -5 is represented using the following steps:
(i) +5 = 0 0101
(ii) Take 1’s complement of 0 0101 and that is
1 1010. MSB is 1 which indicates that number is
negative.
• MSB is always 1 in case of negative numbers.
T.Srikrishna, M.Sc, M.Tech. GVP

12. • Note that drawback of this system is that 0
has two different representation
• one is -0 (e.g., 1 1111 in five bit register) and
second is +0 (e.g., 0 0000 in five bit register).
T.Srikrishna, M.Sc, M.Tech. GVP

13. 2.(c) 2’s Complement Method
• Positive numbers are represented in the same
way as they are represented in sign magnitude
method.
• If the number is negative then it is
represented using 2’s complement.
• First represent the number with positive sign
and then take 2’s complement of that number.
T.Srikrishna, M.Sc, M.Tech. GVP

14. 2's complement
• The 2's complement of binary number is
obtained by adding 1 to the Least Significant
Bit (LSB) of 1's complement of the number.
• 2's complement = 1's complement + 1
• Example of 2's Complement is as follows.
T.Srikrishna, M.Sc, M.Tech. GVP

15. • Example: Let we are using 5 bits registers. The
representation of -5 and +5 will be as follows:
T.Srikrishna, M.Sc, M.Tech. GVP

16. • +5 is represented as it is represented in sign
magnitude method.
• -5 is represented using the following steps:
(i) +5 = 0 0101
(ii) Take 2’s complement of 0 0101 and that is
1 1011. MSB is 1 which indicates that number is
negative.
• MSB is always 1 in case of negative numbers.
T.Srikrishna, M.Sc, M.Tech. GVP

17. • The advantage of this system is that 0 has only
one representation for -0 and +0.
• Zero (0) is considered as always positive (sign
bit is 0) in 2’s complement representation.
Therefore, it is unique or unambiguous
representation.
T.Srikrishna, M.Sc, M.Tech. GVP