Number systems worksheet with answers

Free printable Number systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
place values112806403201608040201

Convert the binary number 1000 0000₂ to decimal. Find N.

1000 0000₂
N =
2.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x29. What is the pattern's value N in decimal?

0x29
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −67 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −678 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −11 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −118 bit
U =
5.Hard
32 bit1 px640 px480 pxM = ? KiB

An uncompressed image is 640 × 480 pixels with 32 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?

640 × 480 px32 bit/px1 KiB = 1024 B
M = KiB
6.Hard
213 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 213 items its own binary code of the same length. What is the smallest number of bits b needed?

213
b = bit

Answer key

  1. 1. N = 128
  2. 2. N = 41
  3. 3. U = 189
  4. 4. U = 245
  5. 5. M = 1200 KiB
  6. 6. b = 8 bit

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