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
Original base	Number to convert	Binary	Octal	Hex	Decimal
Binary	110110	110110	66	36	54
Octal	123	1010011	123	53	83
Hex	2D	101101	55	2D	45
Decimal	123	1111011	173	7B	123

Conversions with fractions (max 3 places of precision)

Original base	Number to convert	Base to convert to
Original base	Number to convert	Binary	Octal	Hex	Decimal
Binary	1011.11	1011.11	13.6	B.C	11.75
Octal	12.5	1010.101	12.5	A.A	10.4
Hex	D.8	1101.1	15.4	D.8	13.5
Decimal	7.6	111.100	7.463	7.999	7.6

Non-decimal addition (unlimited bits)

Number system

Example one

Example two

Example three

Binary

100010

+010010

10101010

+01111111

10110101

+01100101

110100

100101001

100011010

Non-decimal subtraction (unlimited bits)

Number system

Example one

Example two

Binary

1011

-0011

1011011

-1000101

1000

10110

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

Number system
Unsigned Binary	One’s complement	Two’s complement	Decimal
-0111	1000	1001	-7
01011	01011	01011	11
-01000	10111	11000	-8
-000111	111000	111001	-7
-01111	10000	10001	-15