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 values012816413211618141211

Convert the binary number 0111 1111₂ to decimal. Find N.

0111 1111₂
N =
2.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x28. What is the pattern's value N in decimal?

0x28
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −118 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −1188 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −99 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −998 bit
U =
5.Hard
10-bit two's complement, N = ??sign?????????

What is the most negative integer N that can be stored in 10-bit two's complement?

10 bit
N =
6.Hard
3297 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 3297 items its own binary code of the same length. What is the smallest number of bits b needed?

3297
b = bit

Answer key

  1. 1. N = 127
  2. 2. N = 40
  3. 3. U = 138
  4. 4. U = 157
  5. 5. N = −512
  6. 6. b = 12 bit

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