Extra practice questions (solutions)

Processor speeds and times between clock pulses

Processor clock speed	Seconds between pulses	Nano-seconds between pulses
1.5 GHz	6.67 x 10^-10	.67
7.14 MHz	1.4 x 10^-7	140
2.2 GHz	4.54 x 10^-10	.45

Integer conversions between binary, octal, hex, decimal

Original base	Number to convert	Base to convert to
		Binary	Octal	Hex	Decimal
Binary	10111000	10111000	270	B8	184
Octal	1751	1111101001	1751	3E9	1001
Hex	1AA2	1101010100010	15242	1AA2	6818
Decimal	123456	11110001001000000	361100	1E240	123456

Conversions with fractions

Original base	Number to convert	Base to convert to
		Binary	Octal	Hex	Decimal
Binary	111.11	111.11	7.6	7.C	7.75
Octal	54.22	101100.010010	54.22	2C.48	44 18/64 (44. 0.28125)
Hex	1AA.B	110101010.1011	652.54	1AA.B	426 11/16 (426. 0.6875)
Decimal	321.5	101000001.1	501.4	141.8	321.5

Non-decimal addition

Number system	Example one	Example two	Example three
Binary	100010 +010010	10101010 +01111111	10110101 +01100101
	110100	100101001	100011010
Octal	177 + 12	123456 + 23457	32 +77
	211	147135	131
Hexadecimal	12 +10	2B9 + FF	ABCDEF +1234567
	22	3B8	1CF1356

Non-decimal subtraction

Number system	Example one	Example two	Example three
Binary	1011 -0011	1011011 -1000101	0001 -0010
	1000	10110	-0001
Octal	101 - 55	4510 - 227	2 -7
	24	4261	-5
Hexadecimal	A1 -10	8EA2 - F2A	A -F
	91	7F78	-5

Non-decimal multiplication

Number system	Example one	Example two
Binary	100 * 11	1011 *101
	1100	110111
Octal	7 *2	512 *123
	16	65376
Hexadecimal	A *2	2A1 *10B
	14	2BDEB

Converting between unsigned binary, one’s complement and two’s complement

Number system
Unsigned Binary	One’s complement	Two’s complement	Decimal
-0111	1000	1001	-7
1011	1011	1011	11
-01000	10111	11000	-8
-000111	111000	111001	-7
-01111	10000	10001	-15