Exercise
1.1	Describe how the following data are represented in computers:
i.	“Hello World”
ii.	241
iii.	36.27
iv.	–28
1.2	Convert the followings to binary equivalent:
i.	15710	ii.	6710
iii.	8410	iv.	5110
v.	2038	vi.	7168
vii.	23678	viii.	5408
ix.	A43B16	x.	6D2916
xi.	76FE16	xii.	410C16
1.3	Convert the followings to decimal equivalent:
i.	101010112	ii.	1010110011012
iii.	1011010110102	iv.	0110110101012
v.	2178	vi.	1058
vii.	3518	viii.	4768
ix.	A2C16	x.	8D916
xi.	71316	xii.	6F0416
1.4	Convert the followings to their binary equivalent:
i.	18.62510	ii.	29.37510
iii.	463.718	iv.	5D3.B416
1.5	Convert the followings to their decimal equivalent:
i.	1101.01112	ii.	101.110112
iii.	51.378	iv.	62.418
v.	1D.2916	vi.	4C.3B16

1.6	Convert the following numbers to their binary equivalents and perform binary arithmetic to find the answers in binary numbers:

i.	(110101112 - 1608 - 5110)  3A16
ii.	(4910 + 1101112)  138  D16
iii.	C316 + 1548  1210  110102
iv.	168 + 11010112  510 - 5616

1.7	Find the binary equivalent of the followings and their corresponding negative numbers using 2’s complement representation:
i.	4710	ii.	2910
iii.	6810	iv.	15610
v.	468	vi.	538
vii.	1438	viii.	2078
ix.	3A416	x.	D516
xi.	8B16	xii.	16F16
1.8	Find the decimal equivalent of the following 2’s complement numbers:
i.	1011012	ii.	0110102
iii.	0011002	iv.	1110012
v.	101101002	vi.	01110101112
vii.	1011100112	viii.	0011010102
1.9	Use the 2’s complement representation to calculate the followings.  Give the answers in decimal numbers.
i.	37910 - 01010110112
ii.	15316 - 27610
iii.	3910 - 5716
iv.	4216 - 0111011112 
v.	1728 - 01101011012
vi.	010101010112 - 6AC16 
vii.	5148 - 40610
viii.	478 - 6116

Review Exercise
1.10	Convert the followings to binary, octal, hexadecimal and decimal where appropriate:
i.	010010112	ii.	0110100111012
iii.	0110001110002	iv.	0110001100102
v.	10010101101110102	vi.	11001010100100112
vii.	10110101011010102	viii.	11010101000110102
ix.	1568	x.	2168
xi.	4368	xii.	20758
xiii	3071318	xiv.	3120618
xv.	1357248	xvi.	1517648
xvii.	87310	xviii.	39310
xix.	79310	xx.	43610
xxi.	10310	xxii.	27310
xxiii.	21710	xxiv.	30110
xxv.	D2A16	xxvi.	E7C16
xxvii.	4E8B16	xxviii.	6DC516
xxix.	3E1B16	xxx.	2C716
xxxi.	3D916 	xxxii.	A3E116

1.11	Use binary arithmetic, calculate the followings.  Convert the results to decimal numbers.

i.	100112  11012	ii.	100112  11012
iii.	12510  1310	iv.	9710  2710
v.	2910  6110	vi.	2610  4010
vii.	7710  1210	viii.	6510  1410
ix.	4210  1310	x.	17110  910
xi.	39  11	xii.	43  13
xiii.	234  6	xiv.	324  9
xv.	12510  510	xvi.	24210  1110
xvii.	33810  1310	xviii.	12610  710
xix.	110011112  10012	xx.	40610  1410
xxi.	45610  1210	xxii.	110011112  10012

1.12	Using 2's complement for negative numbers, calculate the followings and convert the results to decimal numbers.
i.	2310 - 7810	ii.	2810 - 8710
iii.	10310 - 8610	iv.	9510 - 8110
v.	5310 - 2710	vi.	3610 - 9710
vii.	11010 -4910	viii.	4210 - 9310
ix.	3910 -12010	x.	7310 - 5410
xi.	3610 - 9710	xii.	6310 - 4410
xiii.	2810 - 8910	xiv.	5710 - 2710
xv.	3710 - 9810	xvi.	2710 - 7210

1.13	(a)	Convert 2AF16 to decimal numbers.
	(b)	Convert 2508 to binary numbers.
	(c)	Convert 9210 and 4210 to binary numbers.
	(d)	By 2’s complement method, using a 8 bits to calculate 9210 - 4210.

1.14	Convert the decimal numbers to 8-bit binary numbers and use 2’s complement method to calculate:
1910 - 7610
Convert the result to decimal number.

1.15	(a)	By 2’s complement method, calculate the following expression and convert your answer in hexadecimal.  Show each steps clearly

1748 - A516  10112
	(b)	State the advantage of using 2’s complement.

1.16	(a)	Convert 3F416 to octal number.
	(b)	Convert 4378 to binary number.
	(c)	Using 2’s complement, calculate 3F416 - 4378, state your answer in binary.

1.17	Convert the numbers to binary numbers and find the results. Use 2's complement to represent negative numbers.  Convert the result back to decimal numbers.

i.	438 + 2716 - 7210
ii.	000100112 + 4710  - 5B16