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 values325681691

Convert the hexadecimal number 0x389 to decimal. Find N.

0x389A = 10 … F = 15
N =
2.Easy
place values4256F1601

Convert the hexadecimal number 0x4F0 to decimal. Find N.

0x4F0A = 10 … F = 15
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −66 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −668 bit
U =
4.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −45 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −458 bit
U =
5.Hard
1824 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1824 items its own binary code of the same length. What is the smallest number of bits b needed?

1824
b = bit
6.Hard
8 bit1 px512 px512 pxM = ? KiB

An uncompressed image is 512 × 512 pixels with 8 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?

512 × 512 px8 bit/px1 KiB = 1024 B
M = KiB

Answer key

  1. 1. N = 905
  2. 2. N = 1264
  3. 3. U = 190
  4. 4. U = 211
  5. 5. b = 11 bit
  6. 6. M = 256 KiB

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