Question

Calculate the following issues in bit-level (signed values, two complement arithmetics)

a) 13 + 9 (use word lengths of 5 and 6 bits including the sign bit)

b) 11 – 17 (8-bit word length)

c) 9 * 5 (8-bit word length)

d) a-task using saturative arithmetics

Answer 1

All operations performed in binary format is shown in below

(a) Operation13+9 using word length=5

13 +	0	1	1	0	1
9	0	1	0	0	1
= -10	1	0	1	1	0

Operation13+9 using word length=6

13+	0	0	1	1	0	1
9	0	0	1	0	0	1
=22	0	1	0	1	1	0

(b)Operation11-7 using word length=8

11	0	0	0	0	1	0	1	1
-7	1	1	1	1	1	0	0	1
=4	0	0	0	0	0	1	0	0

(c)Operation9*5 using word length=8

9 *	0	0	0	0	1	0	0	1
5	0	0	0	0	0	1	0	1
=45	0	0	1	0	1	1	0	1

(d)Saturation arithmetic is a version of arithmetic in which all operations such as addition and multiplication are limited to a fixed range between a minimum and maximum value.If the result of an operation is greater than the maximum, it is set to the maximum; if it is below the minimum, it is set to the minimum.

Operation13+9 using word length=5 using saturation arithmetic

here maximum value is 2⁴ -1=15 and minimum value is -2⁴ = -16

13+	0	1	1	0	1
9	0	1	0	0	1
=15	0	1	1	1	1