Answers
1.1
1.2	
i.	100111012	ii.	10000112
iii.	10101002	iv.	1100112
v.	100000112	vi.	1110011102
vii.	100111101112	viii.	1011000002
ix.	10100100001110112	x.	1101101001010012
xi.	1110110111111102	xii.	1000001000011002
1.3
i.	17110	ii.	276510
iii.	290610	iv.	174910
v.	14310	vi.	6910
vii.	23310	viii.	31810
ix.	260410	x.	226510
xi.	181110	xii.	2842010
1.4	
i.	10010.1012	ii.	11101.0112
iii.	100110011.1110012	iv.	010111010011.1011012
1.5
i.	13.437510	ii.	5.8437510
iii.	41.48437510	iv.	50.51562510
v.	29.1601562510	vi.	76.2304687510
1.6
i.	(110101112 - 1608 - 5110) * 3A16
	1608	= 11100002
	5110 	= 1100112
	3A16	= 1110102

				1	1	0	1	0	1	1	1	
			-		1	1	1	0	0	0	0	
					1	1	0	0	1	1	1	
			-			1	1	0	0	1	1	
						1	1	0	1	0	0	
x						1	1	1	0	1	0	
					1	1	0	1	0	0		
			1	1	0	1	0	0				
		1	1	0	1	0	0					
	1	1	0	1	0	0						
1	0	1	1	1	1	0	0	1	0	0	0	

	Answer = 1011110010002

ii.	(4910 + 1101112) * 138 / D16
	4910 	= 1100012
	138	= 10112
	D16	= 11012

									1	1	0	0	0	1	
							+		1	1	0	1	1	1	
								1	1	0	1	0	0	0	
				x							1	0	1	1	
								1	1	0	1	0	0	0	
							1	1	0	1	0	0	0		
					1	1	0	1	0	0	0				
				1	0	0	0	1	1	1	1	0	0	0	
															
								1	0	1	1	0	0	0	
1	1	0	1	1	0	0	0	1	1	1	1	0	0	0	
					1	1	0	1							
						1	0	0	1	1					
							1	1	0	1					
								1	1	0	1				
								1	1	0	1				

	Answer = 10110002

iii.	C316 + 1548 / 1210 * 110102
	C316	= 110000112
	1548	= 11011002
	1210 	= 11002

							1	0	0	1	
1	1	0	0	1	1	0	1	1	0	0	
				1	1	0	0				
							1	1	0	0	
							1	1	0	0	
											
							1	0	0	1	
		x				1	1	0	1	0	
						1	0	0	1		
				1	0	0	1				
			1	0	0	1					
			1	1	1	0	1	0	1	0	
		+	1	1	0	0	0	0	1	1	
		1	1	0	1	0	1	1	0	1	

	Answer = 1101011012

iv.	168 + 11010112 * 510 - 5616
	168	= 11102
	510 	= 1012
	5616	= 10101102

				1	1	0	1	0	1	1	
	x							1	0	1	
				1	1	0	1	0	1	1	
		1	1	0	1	0	1	1			
	1	0	0	0	0	1	0	1	1	1	
+							1	1	1	0	
	1	0	0	0	1	0	0	1	0	1	
-				1	0	1	0	1	1	0	
		1	1	1	0	0	1	1	1	1	

	Answer = 1110011112

1.7
i.	4710 =	01011112	-4710 =	10100012
ii.	2910 =	0111012	-2910 =	1000112
iii.	6810 =	010001002	-6810 =	101111002
iv.	15610 =	0100111002	-15610 =	1011001002
v.	468 =	01001102	-468 =	10110102
vi.	538 =	01010112	-538 =	10101012
vii.	1438 =	011000112	-1438 =	100111012
viii.	2078 =	0100001112	-2078 =	1011110012
ix.	3A416 =	011101001002	-3A416 =	100010111002
x.	D516 =	0110101012	-D516 =	1001010112
xi.	8B16 =	0100010112	-8B16 =	1011101012
xii.	16F16 =	01011011112	-16F16 =	10100100012

1.8
i.	1011012 =	-1910	ii.	0110102 =		2610	
iii.	0011002 =	1210	iv.	1110012 =		-710	
v.	101101002 =	-7610	vi.	01110101112 =	47110	
vii.	1011100112 =	-14110	viii.	0011010102 =	10610	

1.9	i.	37910 - 01010110112 
37910 = 		01011110112	
01010110112 =		01010110112	
			
1's complement of 0101011011		1010100100	
	+	1	
2's complement of 0101011011 (-01010110112)		1010100101	
(+37910)	+	0101111011	
37910 - 01010110112 (+ve)	1	0000100000	
	
carry	
00001000002 =		3210	

	Answer = 00001000002 = 3210

ii.	15316 - 27610
15316 = 		01010100112	
27610 =		01000101002	
			
1's complement of 0100010100		1011101011	
	+	1	
2's complement of 0100010100 (-27610)		1011101100	
(+ 15316)	+	0101010011	
15316 - 27610 (+ve)	1	0000111111	
	
carry	
00001111112 =		6310	

	Answer = 00001111112 = 6310

iii.	3910 - 5716
3910 = 		001001112	
5716 =		010101112	
			
1's complement of 01010111		10101000	
	+	1	
2's complement of 01010111 (-5716)		10101001	
(+ 3910)	+	00100111	
3910 - 5716 (-ve)		11010000	
			
1�s complement of 11010000		00101111	
	+	1	
2�s complement of 11010000		00110000	
			
001100002 =		4810	

	Answer = 110100002 = -4810

iv.	4216 - 0111011112 
4216 =		0010000102	
0111011112 =		0111011112	
			
1's complement of 011101111		100010000	
	+	1	
2's complement of 011101111 (-0111011112)		100010001	
(+ 4216)	+	001000010	
4216 - 0111011112 (-ve)		101010011	
			
1�s complement of 101010011		010101100	
	+	1	
2�s complement of 101010011		010101101	
			
0101011012 =		17310	

	Answer = 1010100112 = -17310

v.	1728 - 01101011012
1728 = 		00011110102	
01101011012 =		01101011012	
			
1's complement of 0110101101		1001010010	
	+	1	
2's complement of 0110101101 (-01101011012)		1001010011	
(+ 1728)	+	0001111010	
1728 - 01101011012 (-ve)		1011001101	
			
1�s complement of 1011001101		0100110010	
	+	1	
2�s complement of 1011001101		0100110011	
			
01001100112 =		30710	

	Answer = 10110011012 = -30710

vi.	010101010112 - 6AC16 
010101010112 = 		0010101010112	
6AC16 =		0110101011002	
			
1's complement of 011010101100		100101010011	
	+	1	
2's complement of 011010101100 (-6AC16)		100101010100	
(+010101010112)	+	001010101011	
010101010112 - 6AC16 (-ve)		101111111111	
			
1�s complement of 101111111111		010000000000	
	+	1	
2�s complement of 101111111111		010000000001	
			
0100000000012 =		102510	

	Answer = 1011111111112 = -102510

vii.	5148 - 40610
5148 = 		01010011002	
40610 =		01100101102	
			
1's complement of 0110010110		1001101001	
	+	1	
2's complement of 0110010110 (-40610)		1001101010	
(+ 5148)	+	0101001100	
5148 - 40610 (-ve)		1110110110	
			
1�s complement of 1110110110		0001001001	
	+	1	
2�s complement of 1110110110		0001001010	
			
00010010102 =		7410	

	Answer = 11101101102 = -7410

viii.	478 - 6116

478 = 		001001112	
6116 =		011000012	
			
1's complement of 01100001		10011110	
	+	1	
2's complement of 01100001 (-6116)		10011111	
(+ 478)	+	00100111	
478 - 6116 (-ve)		11000110	
			
1�s complement of 11000110		00111001	
	+	1	
2�s complement of 11000110		00111010	
			
001110102 =		5810	

	Answer = 110001102 = -5810

Selected Answers for Review Exercises
1.10
	Binary	Octal	Hexadecimal	Decimal	
i		113	4B	75	
ii		3235	69D	1693	
iii		3070	638	1592	
iv		3062	632	1586	
v		112672	95BA	38330	
vi		145223	CA93	51859	
vii		132552	B56A	46442	
viii		152432	D51A	54554	
ix	1101110		6E	110	
x	10001110		8E	142	
xi	100011110		11E	286	
xii	10000111101		43D	1085	
xiii	11000111001011001		18E59	101977	
xiv	11001010000110001		19431	103473	
xv	1011101111010100		BBD4	48084	
xvi	1101001111110100		D3F4	54260	
xvii	1101101001	1551	369		
xviii	110001001	611	189		
xix	1100011001	1431	319		
xx	110110100	664	164		
xxi	1100111	147	67		
xxii	100010001	421	111		
xxiii	11011001	331	D9		
xxiv	100101101	455	12D		
xxv	110100101010	6452		3370	
xxvi	111001111100	7174		3708	
xxvii	100111010001011	47213		20107	
xxviii	110110111000101	66705		28101	
xxix	11111000011011	37033		15899	
xxx	1011000111	1307		711	
xxxi	1111011001	1731		985	
xxxii	1010001111100001	121741		41953	

1.16
i.	438 	= 	1000112
	2716 	=	001001112
	7210	=	10010002	
					[conversion: 1 each]
	00100011	(438)
+	00100111	(2716)
		01001010	(438 + 2716)
		[Calculation: 1]
	1�s complement of 7210 	= 11111111 - 1001000 
		= 10110111
	2�s complement of 7210  	= 10111000	(-7210)
		[2�s complement: 2]
	01001010	(438 + 2716)
+	10111000	(-7210)
         	       	00000010	(438 + 2716 - 7210)
		[Calculation: 3]

Ans : 102 = 210
					[answer: 1]
ii.	
	 4710 	=	1011112
	5B16  	=	010110112
					[conversion: 1 each]

	00010011	(000100112)
+	00101111	(4710 )
		01000010	(000100112 + 4710)
		[Calculation: 1]
1�s complement of 5B16  :	10100100
2�s complement of 5B16  :	10100101	(-5B16)
		[2�s complement: 2]
	01000010	(000100112 + 4710)
+	10100101	(-5B16)
		11100111	answer is negative
		[Calculation: 2]
1�s complement of answer:	00011000
2�s complement of answer:	00011001
		[2�s complement: 2]
000110012	=	2510
Answer:	-25
					[answer: 1]