ECE 1331 Workshop

Numbering Systems

Diana de la Rosa-Pohl

ECE 2300 WorkshopUniversity of Houston

2

Part I: Give the prefix names and abbreviations for the

following powers of 2:

Give the power of 2 for the following prefix names:

2n Prefix name Abbreviation

250

220

270

Prefix name 2n

Exa

Giga

Yotta

ECE 2300 WorkshopUniversity of Houston

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Part II: Calculate the following powers of 2: (Give exact

numbers. Do not use abbreviations).

1. 27 =

2. 210 =

3. 23 =

Calculate the following, and write the prefix name of the answer:

solveNumerical Value ( NOT

in the 2n form!!)Value using Prefix name

210 × 210

29 + 29

225 × 215

ECE 2300 WorkshopUniversity of Houston

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Part III: Fill in:

1. Binary to decimal:

i. 1002 = (1 × 2^2) + (0 × 2^_) + (0 × _^_) = _ + _ + _ = ____

ii. 11112 = (_ × 2^_) + (_ × 2^_) + (_ × 2^_) + (_ × 2^_)

= _ + _ + _ + _ = ____

2. Decimal to binary:

i. 510 What is the highest power of 2 that fits into 5? _____

Make your digit placeholders beginning with that power of 2.

510 = ________

i. 1310 What is the highest power of 2 that fits into 13? ____

Make your digit placeholders beginning with that power of 2.

1310 = ________

ECE 2300 WorkshopUniversity of Houston

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Part IV: Fill in:

1. Decimal to hexadecimal:

i. 2610 = (break into multiples of powers of 16) ____ + ____ =

(_ × 16^1) + (_ × 16^0) = _____

i. 4010 = (break into multiples of powers of 16) ____ + ____ =

(_ × 16^1) + (_ × 16^0) = _____

2. Hexadecimal to decimal:

i. 1316 = (take nibble by nibble, converting each nibble to

decimal) (1 × 16^1) + (3 × 16^0) = ____ + ____ = _____

ii. 2E16 = (take nibble by nibble, converting each nibble to

decimal) (_ × 16^1) + (_ × 16^0) = ____ + ____ = _____

ECE 2300 WorkshopUniversity of Houston

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Part V: Fill in:

1. Binary to hexadecimal: (nibble by nibble)

i. 11102 = _×23 + _×22 + _×21 + _×20 = _ + _ + _ + _

= _____

ii. 110102 = (separate into nibbles) _____ _____ =

(_×23 + _×22 + _×21 + _×20 ) (_×23 + _×22 + _×21 + _×20 ) =

____ ____

2. Hexadecimal to binary: (nibble by nibble)

i. A16 = __ (23) __ (22) __ (21) __ (20) = __ __ __ __

ii. F516 =

left nibble : __ (23) __ (22) __ (21) __ (20) = __ __ __ __right nibble : __ (23) __ (22) __ (21) __ (20) = __ __ __ __

= __ __ __ __ __ __ __ __

Part VI: Do the following conversions:

ECE 2300 WorkshopUniversity of Houston

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Decimal (Base 10) Binary (Base 2)

1210

100002

Decimal (Base 10) Hexadecimal (Base 16)

1510

1B16

Hexadecimal (Base 16) Binary (Base 2)

2316

10002

ECE 2300 WorkshopUniversity of Houston

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Part VII:

Decimal Binary Hexadecimal

_ 101 5

6 ___ 6

7 111 _

8 ____ 8

9 1001 _

10 1010 _

__ 1011 B

__ ____ _

Fill the following series:

ECE 2300 WorkshopUniversity of Houston

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Part VIII: Do the following additions:

1. Binary:

1 101 1100 + 1 + 111 +1011 ----- -------- --------

2. Hexadecimal:

A 1D 25A + 3 + 13 + 7B0 ----- ------ --------