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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1.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0xA2. What is the pattern's value N in decimal?

0xA2
N =
2.Easy
place values112816403211618140211

Convert the binary number 1101 1101₂ to decimal. Find N.

1101 1101₂
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −97 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −978 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −86 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −868 bit
U =
5.Hard
1410 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1410 items its own binary code of the same length. What is the smallest number of bits b needed?

1410
b = bit
6.Hard
24-bit two's complement, N = ??sign???????????????????????

What is the most negative integer N that can be stored in 24-bit two's complement?

24 bit
N =

Answer key

  1. 1. N = 162
  2. 2. N = 221
  3. 3. U = 159
  4. 4. U = 170
  5. 5. b = 11 bit
  6. 6. N = −8.389 × 10⁶

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